137:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000
Ejemplo 1  :@0.096359:0.133446:0.172968:0.133446:0.172968:0.118333:0.096359:0.118333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Obtenemos:@0.172966:0.133760:0.266339:0.133760:0.266339:0.116860:0.172966:0.116860:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 las potencias de los siguientes números racionales.:@0.266339:0.133760:0.641796:0.133760:0.641796:0.118091:0.266339:0.118091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a)  :@0.124851:0.169802:0.157063:0.169802:0.157063:0.152667:0.124851:0.152667:0.000000:0.000000:0.000000:0.000000
1:@0.168443:0.161482:0.178219:0.161482:0.178219:0.144448:0.168443:0.144448:0.000000
3:@0.167823:0.182502:0.177599:0.182502:0.177599:0.165467:0.167823:0.165467:0.000000
3:@0.189159:0.151616:0.195713:0.151616:0.195713:0.140195:0.189159:0.140195:0.000000
   :@0.198549:0.169806:0.220699:0.169806:0.220699:0.152670:0.198549:0.152670:0.000000:0.000000:0.000000
        b)     :@0.277290:0.169806:0.342339:0.169806:0.342339:0.152670:0.277290:0.152670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.365970:0.160982:0.375526:0.160982:0.375526:0.144332:0.365970:0.144332:0.000000
3:@0.366186:0.181528:0.375742:0.181528:0.375742:0.164878:0.366186:0.164878:0.000000
4:@0.387777:0.151339:0.394184:0.151339:0.394184:0.140176:0.387777:0.140176:0.000000
 :@0.399293:0.169806:0.403015:0.169806:0.403015:0.152670:0.399293:0.152670:0.000000
 :@0.458211:0.169806:0.461934:0.169806:0.461934:0.152670:0.458211:0.152670:0.000000
 :@0.518521:0.169806:0.522244:0.169806:0.522244:0.152670:0.518521:0.152670:0.000000
 :@0.578829:0.169806:0.582552:0.169806:0.582552:0.152670:0.578829:0.152670:0.000000
c)     :@0.639147:0.169806:0.671856:0.169806:0.671856:0.152670:0.639147:0.152670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.696483:0.160982:0.706039:0.160982:0.706039:0.144332:0.696483:0.144332:0.000000
4:@0.696267:0.181528:0.705823:0.181528:0.705823:0.164878:0.696267:0.164878:0.000000
3:@0.718345:0.151339:0.724752:0.151339:0.724752:0.140176:0.718345:0.140176:0.000000
Solución:@0.096359:0.204073:0.157020:0.204073:0.157020:0.188960:0.096359:0.188960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a)  :@0.124851:0.235403:0.157063:0.235403:0.157063:0.218267:0.124851:0.218267:0.000000:0.000000:0.000000:0.000000
×× =:@0.173159:0.234824:0.237305:0.234824:0.237305:0.219251:0.173159:0.219251:0.000000:0.000000:0.000000:0.000000
1 1 1:@0.161328:0.225184:0.223823:0.225188:0.223823:0.209518:0.161328:0.209514:0.000000:0.000000:0.000000:0.000000:0.000000
3 3 3:@0.160752:0.244637:0.223247:0.244637:0.223247:0.228967:0.160752:0.228967:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.247392:0.225188:0.256385:0.225188:0.256385:0.209518:0.247392:0.209518:0.000000
27:@0.242053:0.244637:0.259836:0.244637:0.259836:0.228967:0.242053:0.228967:0.000000:0.000000
          b)     :@0.267312:0.235403:0.342331:0.235403:0.342331:0.218267:0.267312:0.218267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.364871:0.222543:0.373983:0.222543:0.373983:0.206666:0.364871:0.206666:0.000000
3:@0.365077:0.242132:0.374188:0.242132:0.374188:0.226256:0.365077:0.226256:0.000000
2:@0.423217:0.222543:0.432328:0.222543:0.432328:0.206666:0.423217:0.206666:0.000000
3:@0.423422:0.242132:0.432533:0.242132:0.432533:0.226256:0.423422:0.226256:0.000000
2:@0.481562:0.222543:0.490673:0.222543:0.490673:0.206666:0.481562:0.206666:0.000000
3:@0.481767:0.242132:0.490878:0.242132:0.490878:0.226256:0.481767:0.226256:0.000000
2:@0.539907:0.222543:0.549018:0.222543:0.549018:0.206666:0.539907:0.206666:0.000000
3:@0.540113:0.242132:0.549224:0.242132:0.549224:0.226256:0.540113:0.226256:0.000000
=:@0.562980:0.232142:0.573230:0.232142:0.573230:0.213884:0.562980:0.213884:0.000000
16:@0.576778:0.222544:0.594795:0.222544:0.594795:0.206668:0.576778:0.206668:0.000000:0.000000
81:@0.578887:0.242133:0.596904:0.242133:0.596904:0.226257:0.578887:0.226257:0.000000:0.000000
  :@0.608193:0.235403:0.615638:0.235403:0.615638:0.218267:0.608193:0.218267:0.000000:0.000000
c)     :@0.639133:0.235403:0.671842:0.235403:0.671842:0.218267:0.639133:0.218267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.695395:0.222588:0.704528:0.222588:0.704528:0.205942:0.695395:0.205942:0.000000
4:@0.695189:0.242225:0.704322:0.242225:0.704322:0.225580:0.695189:0.225580:0.000000
3:@0.755371:0.222588:0.764505:0.222588:0.764505:0.205942:0.755371:0.205942:0.000000
4:@0.755166:0.242225:0.764299:0.242225:0.764299:0.225580:0.755166:0.225580:0.000000
3:@0.815348:0.222588:0.824482:0.222588:0.824482:0.205942:0.815348:0.205942:0.000000
4:@0.815142:0.242225:0.824276:0.242225:0.824276:0.225580:0.815142:0.225580:0.000000
=:@0.839008:0.232210:0.849283:0.232210:0.849283:0.213907:0.839008:0.213907:0.000000
27:@0.866550:0.222588:0.884611:0.222588:0.884611:0.205942:0.866550:0.205942:0.000000:0.000000
64:@0.866550:0.242225:0.884611:0.242225:0.884611:0.225580:0.866550:0.225580:0.000000:0.000000
Propiedades de la potenciación:@0.096359:0.277784:0.423085:0.277784:0.423085:0.255975:0.096359:0.255975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si :@0.096359:0.304652:0.112428:0.304652:0.112428:0.288982:0.096359:0.288982:0.000000:0.000000:0.000000
a:@0.118730:0.297114:0.127999:0.297114:0.127999:0.280753:0.118730:0.280753:0.000000
}:@0.113511:0.305356:0.133229:0.305356:0.133229:0.291677:0.113511:0.291677:0.000000
b:@0.118735:0.314710:0.128004:0.314710:0.128004:0.298349:0.118735:0.298349:0.000000
 :@0.134307:0.304655:0.138342:0.304655:0.138342:0.288986:0.134307:0.288986:0.000000
∈ :@0.138158:0.312471:0.153508:0.312471:0.153508:0.293472:0.138158:0.293472:0.000000:0.000000
Q:@0.153324:0.307670:0.167661:0.307670:0.167661:0.287257:0.153324:0.287257:0.000000
; b ≠ 0, m, n   :@0.167476:0.304655:0.269179:0.304655:0.269179:0.288986:0.167476:0.288986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∈:@0.253847:0.312471:0.265327:0.312471:0.265327:0.293472:0.253847:0.293472:0.000000
Z:@0.268994:0.307670:0.281285:0.307670:0.281285:0.287257:0.268994:0.287257:0.000000
+:@0.281109:0.303161:0.289135:0.303161:0.289135:0.292084:0.281109:0.292084:0.000000
 se cumplen las siguientes propiedades::@0.289028:0.304652:0.573348:0.304652:0.573348:0.288982:0.289028:0.288982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Radicación con números racionales:@0.096359:0.673280:0.461523:0.673280:0.461523:0.651471:0.096359:0.651471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La radicación es el proceso inverso a la potenciación y nos permite determinar la base de una potencia dada. :@0.096359:0.696061:0.907488:0.696061:0.907488:0.680391:0.096359:0.680391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, :@0.096359:0.723970:0.189898:0.723970:0.189898:0.708301:0.096359:0.708301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
8:@0.210391:0.714700:0.218566:0.714700:0.218566:0.700455:0.210391:0.700455:0.000000
27:@0.206354:0.734151:0.222536:0.734151:0.222536:0.719905:0.206354:0.719905:0.000000:0.000000
3:@0.194791:0.719651:0.199185:0.719651:0.199185:0.711994:0.194791:0.711994:0.000000
es   porque :@0.229733:0.723973:0.326296:0.723973:0.326296:0.708303:0.229733:0.708303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.253163:0.715957:0.261338:0.715957:0.261338:0.701712:0.253163:0.701712:0.000000
3:@0.253319:0.735407:0.261494:0.735407:0.261494:0.721161:0.253319:0.721161:0.000000
2:@0.338094:0.714193:0.346270:0.714193:0.346270:0.699948:0.338094:0.699948:0.000000
3:@0.338245:0.733531:0.346420:0.733531:0.346420:0.719286:0.338245:0.719286:0.000000
3:@0.357517:0.705432:0.361911:0.705432:0.361911:0.697776:0.357517:0.697776:0.000000
= :@0.366131:0.723973:0.380965:0.723973:0.380965:0.708303:0.366131:0.708303:0.000000:0.000000
8:@0.398472:0.714266:0.406647:0.714266:0.406647:0.700021:0.398472:0.700021:0.000000
27:@0.394434:0.733604:0.410617:0.733604:0.410617:0.719358:0.394434:0.719358:0.000000:0.000000
.:@0.422448:0.723145:0.425363:0.723145:0.425363:0.708900:0.422448:0.708900:0.000000
Propiedad:@0.146026:0.343169:0.223774:0.343169:0.223774:0.327591:0.146026:0.327591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Expresión algebraica:@0.351813:0.343169:0.507475:0.343169:0.507475:0.327591:0.351813:0.327591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplos:@0.708790:0.343169:0.777341:0.343169:0.777341:0.327591:0.708790:0.327591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Producto de potencias :@0.103995:0.375431:0.264682:0.375431:0.264682:0.360319:0.103995:0.360319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de bases iguales:@0.103995:0.390519:0.217777:0.390519:0.217777:0.375406:0.103995:0.375406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.358881:0.374475:0.366465:0.374475:0.366465:0.361880:0.358881:0.361880:0.000000
b:@0.358685:0.391878:0.366269:0.391878:0.366269:0.379284:0.358685:0.379284:0.000000
m:@0.376926:0.366872:0.384558:0.366872:0.384558:0.358843:0.376926:0.358843:0.000000
a:@0.409719:0.374475:0.417303:0.374475:0.417303:0.361880:0.409719:0.361880:0.000000
b:@0.409523:0.391878:0.417107:0.391878:0.417107:0.379284:0.409523:0.379284:0.000000
n:@0.427953:0.366872:0.432912:0.366872:0.432912:0.358843:0.427953:0.358843:0.000000
=:@0.437047:0.382954:0.445325:0.382954:0.445325:0.368209:0.437047:0.368209:0.000000
a:@0.458487:0.374478:0.466071:0.374478:0.466071:0.361884:0.458487:0.361884:0.000000
b:@0.458291:0.391882:0.465875:0.391882:0.465875:0.379287:0.458291:0.379287:0.000000
m   n:@0.476529:0.366872:0.498501:0.366872:0.498501:0.358843:0.476529:0.358843:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.486142:0.367182:0.491419:0.367182:0.491419:0.357783:0.486142:0.357783:0.000000
2:@0.637917:0.374475:0.645275:0.374475:0.645275:0.361654:0.637917:0.361654:0.000000
3:@0.638053:0.391878:0.645410:0.391878:0.645410:0.379057:0.638053:0.379057:0.000000
3:@0.655351:0.366872:0.660042:0.366872:0.660042:0.358699:0.655351:0.358699:0.000000
2:@0.684609:0.374475:0.691967:0.374475:0.691967:0.361654:0.684609:0.361654:0.000000
3:@0.684745:0.391878:0.692103:0.391878:0.692103:0.379057:0.684745:0.379057:0.000000
2:@0.702044:0.366872:0.706734:0.366872:0.706734:0.358699:0.702044:0.358699:0.000000
=:@0.710947:0.382954:0.719225:0.382954:0.719225:0.368209:0.710947:0.368209:0.000000
2:@0.732055:0.374478:0.739413:0.374478:0.739413:0.361658:0.732055:0.361658:0.000000
3:@0.732191:0.391882:0.739549:0.391882:0.739549:0.379061:0.732191:0.379061:0.000000
3:@0.749490:0.366872:0.754180:0.366872:0.754180:0.358699:0.749490:0.358699:0.000000
   :@0.754815:0.366872:0.764364:0.366872:0.764364:0.358843:0.754815:0.358843:0.000000:0.000000:0.000000
+:@0.756839:0.367182:0.762116:0.367182:0.762116:0.357783:0.756839:0.357783:0.000000
2:@0.765181:0.366872:0.769871:0.366872:0.769871:0.358699:0.765181:0.358699:0.000000
=:@0.774084:0.382954:0.782361:0.382954:0.782361:0.368209:0.774084:0.368209:0.000000
2:@0.795192:0.374478:0.802550:0.374478:0.802550:0.361658:0.795192:0.361658:0.000000
3:@0.795328:0.391882:0.802685:0.391882:0.802685:0.379061:0.795328:0.379061:0.000000
5:@0.812624:0.366872:0.817315:0.366872:0.817315:0.358699:0.812624:0.358699:0.000000
=:@0.821341:0.382954:0.829618:0.382954:0.829618:0.368209:0.821341:0.368209:0.000000
32:@0.837307:0.374478:0.851872:0.374478:0.851872:0.361658:0.837307:0.361658:0.000000:0.000000
243:@0.833870:0.391882:0.855641:0.391882:0.855641:0.379061:0.833870:0.379061:0.000000:0.000000:0.000000
Cociente de potencias :@0.103985:0.425892:0.262092:0.425892:0.262092:0.410779:0.103985:0.410779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de bases iguales:@0.103985:0.440979:0.217767:0.440979:0.217767:0.425867:0.103985:0.425867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.363112:0.424309:0.370696:0.424309:0.370696:0.411715:0.363112:0.411715:0.000000
b:@0.362916:0.441712:0.370500:0.441712:0.370500:0.429118:0.362916:0.429118:0.000000
m:@0.381158:0.416707:0.388790:0.416707:0.388790:0.408678:0.381158:0.408678:0.000000
÷:@0.392700:0.432787:0.400978:0.432787:0.400978:0.418043:0.392700:0.418043:0.000000
a:@0.413477:0.424311:0.421061:0.424311:0.421061:0.411717:0.413477:0.411717:0.000000
b:@0.413281:0.441715:0.420865:0.441715:0.420865:0.429121:0.413281:0.429121:0.000000
n:@0.431713:0.416707:0.436673:0.416707:0.436673:0.408678:0.431713:0.408678:0.000000
=:@0.440807:0.432787:0.449084:0.432787:0.449084:0.418043:0.440807:0.418043:0.000000
a:@0.462246:0.424311:0.469830:0.424311:0.469830:0.411717:0.462246:0.411717:0.000000
b:@0.462050:0.441715:0.469634:0.441715:0.469634:0.429121:0.462050:0.429121:0.000000
m - n:@0.480290:0.416707:0.498822:0.416707:0.498822:0.408678:0.480290:0.408678:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.655284:0.446826:0.658953:0.446826:0.658953:0.432581:0.655284:0.432581:0.000000
5:@0.670048:0.424475:0.677406:0.424475:0.677406:0.411654:0.670048:0.411654:0.000000
7:@0.669581:0.441878:0.676938:0.441878:0.676938:0.429058:0.669581:0.429058:0.000000
7:@0.687104:0.416872:0.691794:0.416872:0.691794:0.408699:0.687104:0.408699:0.000000
÷:@0.695820:0.432953:0.704097:0.432953:0.704097:0.418208:0.695820:0.418208:0.000000
5:@0.716415:0.424477:0.723773:0.424477:0.723773:0.411657:0.716415:0.411657:0.000000
7:@0.715948:0.441881:0.723306:0.441881:0.723306:0.429060:0.715948:0.429060:0.000000
4:@0.734032:0.416872:0.738723:0.416872:0.738723:0.408699:0.734032:0.408699:0.000000
=:@0.743313:0.432953:0.751590:0.432953:0.751590:0.418208:0.743313:0.418208:0.000000
5:@0.764557:0.424477:0.771914:0.424477:0.771914:0.411657:0.764557:0.411657:0.000000
7:@0.764089:0.441881:0.771447:0.441881:0.771447:0.429060:0.764089:0.429060:0.000000
3:@0.781807:0.416872:0.786497:0.416872:0.786497:0.408699:0.781807:0.408699:0.000000
=:@0.790525:0.432953:0.798802:0.432953:0.798802:0.418208:0.790525:0.418208:0.000000
125:@0.802586:0.424477:0.824358:0.424477:0.824358:0.411657:0.802586:0.411657:0.000000:0.000000:0.000000
343:@0.803054:0.441881:0.824825:0.441881:0.824825:0.429060:0.803054:0.429060:0.000000:0.000000:0.000000
Potencia de una :@0.103985:0.479753:0.219409:0.479753:0.219409:0.464641:0.103985:0.464641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
potencia:@0.103985:0.494841:0.165349:0.494841:0.165349:0.479728:0.103985:0.479728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.385685:0.478148:0.393268:0.478148:0.393268:0.465553:0.385685:0.465553:0.000000
b:@0.385489:0.495551:0.393072:0.495551:0.393072:0.482957:0.385489:0.482957:0.000000
m:@0.403777:0.470263:0.410212:0.470263:0.410212:0.463493:0.403777:0.463493:0.000000
n:@0.419844:0.467610:0.424026:0.467610:0.424026:0.460840:0.419844:0.460840:0.000000
=:@0.428231:0.486626:0.436508:0.486626:0.436508:0.471881:0.428231:0.471881:0.000000
a:@0.449670:0.478150:0.457254:0.478150:0.457254:0.465556:0.449670:0.465556:0.000000
b:@0.449474:0.495554:0.457058:0.495554:0.457058:0.482959:0.449474:0.482959:0.000000
m   n:@0.467761:0.470263:0.486456:0.470263:0.486456:0.463493:0.467761:0.463493:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.658229:0.477664:0.665587:0.477664:0.665587:0.464255:0.658229:0.464255:0.000000
5:@0.658365:0.495067:0.665723:0.495067:0.665723:0.481658:0.658365:0.481658:0.000000
2:@0.675709:0.469778:0.679664:0.469778:0.679664:0.462571:0.675709:0.462571:0.000000
2:@0.689044:0.467127:0.692998:0.467127:0.692998:0.459919:0.689044:0.459919:0.000000
=:@0.697289:0.486142:0.705567:0.486142:0.705567:0.471397:0.697289:0.471397:0.000000
2:@0.718397:0.477666:0.725755:0.477666:0.725755:0.464257:0.718397:0.464257:0.000000
5:@0.718533:0.495070:0.725891:0.495070:0.725891:0.481661:0.718533:0.481661:0.000000
2:@0.735877:0.469778:0.739831:0.469778:0.739831:0.462571:0.735877:0.462571:0.000000
   :@0.740731:0.469778:0.748973:0.469778:0.748973:0.463009:0.740731:0.463009:0.000000:0.000000:0.000000
2:@0.749824:0.469778:0.753779:0.469778:0.753779:0.462571:0.749824:0.462571:0.000000
=:@0.758069:0.486142:0.766346:0.486142:0.766346:0.471397:0.758069:0.471397:0.000000
2:@0.779177:0.477666:0.786534:0.477666:0.786534:0.464257:0.779177:0.464257:0.000000
5:@0.779312:0.495070:0.786670:0.495070:0.786670:0.481661:0.779312:0.481661:0.000000
4:@0.796986:0.469778:0.800941:0.469778:0.800941:0.462571:0.796986:0.462571:0.000000
=:@0.805562:0.486142:0.813839:0.486142:0.813839:0.471397:0.805562:0.471397:0.000000
16:@0.821061:0.477666:0.835625:0.477666:0.835625:0.464257:0.821061:0.464257:0.000000:0.000000
625:@0.818422:0.495070:0.840194:0.495070:0.840194:0.481661:0.818422:0.481661:0.000000:0.000000:0.000000
Potencia con :@0.103985:0.540780:0.197313:0.540780:0.197313:0.525667:0.103985:0.525667:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponente entero :@0.103985:0.555868:0.232642:0.555868:0.232642:0.540755:0.103985:0.540755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
negativo:@0.103985:0.570955:0.165600:0.570955:0.165600:0.555843:0.103985:0.555843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.372514:0.546364:0.380269:0.546364:0.380269:0.532675:0.372514:0.532675:0.000000
b:@0.372313:0.564160:0.380068:0.564160:0.380068:0.550471:0.372313:0.550471:0.000000
m:@0.396699:0.538300:0.403279:0.538300:0.403279:0.530943:0.396699:0.530943:0.000000
1:@0.433898:0.546364:0.441422:0.546364:0.441422:0.532652:0.433898:0.532652:0.000000
a:@0.433127:0.561985:0.440882:0.561985:0.440882:0.548296:0.433127:0.548296:0.000000
b:@0.432927:0.579445:0.440682:0.579445:0.440682:0.565757:0.432927:0.565757:0.000000
m:@0.452977:0.523655:0.459557:0.523655:0.459557:0.516298:0.452977:0.516298:0.000000
=:@0.464009:0.555103:0.472473:0.555103:0.472473:0.542074:0.464009:0.542074:0.000000
=:@0.406764:0.555103:0.415228:0.555103:0.415228:0.542074:0.406764:0.542074:0.000000
b:@0.485732:0.546367:0.493487:0.546367:0.493487:0.532678:0.485732:0.532678:0.000000
a:@0.485917:0.564163:0.493672:0.564163:0.493672:0.550475:0.485917:0.550475:0.000000
m:@0.504432:0.538300:0.511012:0.538300:0.511012:0.530943:0.504432:0.530943:0.000000
2:@0.672596:0.545540:0.679954:0.545540:0.679954:0.532720:0.672596:0.532720:0.000000
5:@0.672732:0.562944:0.680090:0.562944:0.680090:0.550123:0.672732:0.550123:0.000000
3:@0.694646:0.537655:0.698600:0.537655:0.698600:0.530764:0.694646:0.530764:0.000000
1:@0.712691:0.545540:0.720049:0.545540:0.720049:0.532720:0.712691:0.532720:0.000000
2:@0.712073:0.560817:0.719431:0.560817:0.719431:0.547996:0.712073:0.547996:0.000000
5:@0.712224:0.577892:0.719582:0.577892:0.719582:0.565071:0.712224:0.565071:0.000000
3:@0.730878:0.523333:0.734833:0.523333:0.734833:0.516442:0.730878:0.516442:0.000000
=:@0.738936:0.554018:0.747213:0.554018:0.747213:0.539274:0.738936:0.539274:0.000000
5:@0.760179:0.545543:0.767537:0.545543:0.767537:0.532722:0.760179:0.532722:0.000000
2:@0.760044:0.562946:0.767401:0.562946:0.767401:0.550126:0.760044:0.550126:0.000000
3:@0.777523:0.537655:0.781478:0.537655:0.781478:0.530764:0.777523:0.530764:0.000000
=:@0.785579:0.554018:0.793857:0.554018:0.793857:0.539274:0.785579:0.539274:0.000000
125:@0.797174:0.545543:0.818945:0.545543:0.818945:0.532722:0.797174:0.532722:0.000000:0.000000:0.000000
8:@0.804562:0.562946:0.811919:0.562946:0.811919:0.550126:0.804562:0.550126:0.000000
Potencia con :@0.103985:0.607655:0.196391:0.607655:0.196391:0.592542:0.103985:0.592542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
exponente 0 si y solo si :@0.103985:0.622742:0.265528:0.622742:0.265528:0.607630:0.103985:0.607630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a/b es diferente de cero:@0.103985:0.637830:0.265796:0.637830:0.265796:0.622717:0.103985:0.622717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.412281:0.612590:0.419864:0.612590:0.419864:0.599995:0.412281:0.599995:0.000000
b:@0.412085:0.629993:0.419668:0.629993:0.419668:0.617399:0.412085:0.617399:0.000000
0:@0.430373:0.604704:0.434328:0.604704:0.434328:0.597813:0.430373:0.597813:0.000000
=:@0.438760:0.621068:0.447037:0.621068:0.447037:0.606323:0.438760:0.606323:0.000000
1:@0.449027:0.620581:0.456385:0.620581:0.456385:0.607760:0.449027:0.607760:0.000000
8:@0.727041:0.611966:0.734399:0.611966:0.734399:0.599145:0.727041:0.599145:0.000000
24:@0.723272:0.629370:0.737837:0.629370:0.737837:0.616549:0.723272:0.616549:0.000000:0.000000
0:@0.748573:0.604081:0.752528:0.604081:0.752528:0.597190:0.748573:0.597190:0.000000
=:@0.756960:0.620444:0.765237:0.620444:0.765237:0.605700:0.756960:0.605700:0.000000
1:@0.767227:0.619958:0.774585:0.619958:0.774585:0.607137:0.767227:0.607137:0.000000
Propiedades:@0.104810:0.860042:0.186947:0.860042:0.186947:0.844464:0.104810:0.844464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.239770:0.850201:0.247353:0.850201:0.247353:0.837606:0.239770:0.837606:0.000000
b:@0.239574:0.867604:0.247157:0.867604:0.247157:0.855010:0.239574:0.855010:0.000000
n:@0.229026:0.854692:0.233208:0.854692:0.233208:0.847923:0.229026:0.847923:0.000000
m:@0.259181:0.839629:0.265615:0.839629:0.265615:0.832859:0.259181:0.832859:0.000000
=:@0.269971:0.858680:0.278248:0.858680:0.278248:0.843936:0.269971:0.843936:0.000000
a:@0.302673:0.850205:0.310257:0.850205:0.310257:0.837610:0.302673:0.837610:0.000000
m:@0.310867:0.843306:0.317301:0.843306:0.317301:0.836537:0.310867:0.836537:0.000000
b:@0.302480:0.867599:0.310064:0.867599:0.310064:0.855005:0.302480:0.855005:0.000000
m:@0.310679:0.860703:0.317114:0.860703:0.317114:0.853934:0.310679:0.853934:0.000000
n:@0.291926:0.854021:0.296108:0.854021:0.296108:0.847251:0.291926:0.847251:0.000000
m:@0.330467:0.837966:0.336902:0.837966:0.336902:0.831197:0.330467:0.831197:0.000000
×:@0.466312:0.860432:0.475417:0.860432:0.475417:0.846416:0.466312:0.846416:0.000000
×:@0.397758:0.860093:0.406035:0.860093:0.406035:0.847352:0.397758:0.847352:0.000000
=:@0.424188:0.860093:0.432466:0.860093:0.432466:0.847352:0.424188:0.847352:0.000000
a:@0.386209:0.851482:0.393793:0.851482:0.393793:0.838095:0.386209:0.838095:0.000000
b:@0.386028:0.868987:0.393612:0.868987:0.393612:0.855601:0.386028:0.855601:0.000000
c:@0.411041:0.851482:0.417313:0.851482:0.417313:0.838095:0.411041:0.838095:0.000000
d:@0.410242:0.868987:0.417826:0.868987:0.417826:0.855601:0.410242:0.855601:0.000000
a:@0.448402:0.851482:0.455986:0.851482:0.455986:0.838095:0.448402:0.838095:0.000000
b:@0.448206:0.868987:0.455790:0.868987:0.455790:0.855601:0.448206:0.855601:0.000000
c:@0.495699:0.851482:0.501971:0.851482:0.501971:0.838095:0.495699:0.838095:0.000000
d:@0.494900:0.868987:0.502484:0.868987:0.502484:0.855601:0.494900:0.855601:0.000000
n:@0.375377:0.855932:0.379558:0.855932:0.379558:0.848737:0.375377:0.848737:0.000000
n:@0.437567:0.855932:0.441748:0.855932:0.441748:0.848737:0.437567:0.848737:0.000000
n:@0.484075:0.855932:0.488257:0.855932:0.488257:0.848737:0.484075:0.848737:0.000000
a:@0.557552:0.851477:0.565136:0.851477:0.565136:0.838090:0.557552:0.838090:0.000000
b:@0.557356:0.868982:0.564940:0.868982:0.564940:0.855596:0.557356:0.855596:0.000000
c:@0.582656:0.851477:0.588928:0.851477:0.588928:0.838090:0.582656:0.838090:0.000000
d:@0.581857:0.868982:0.589441:0.868982:0.589441:0.855596:0.581857:0.855596:0.000000
a:@0.620017:0.851477:0.627601:0.851477:0.627601:0.838090:0.620017:0.838090:0.000000
b:@0.619821:0.868982:0.627405:0.868982:0.627405:0.855596:0.619821:0.855596:0.000000
c:@0.666847:0.851477:0.673119:0.851477:0.673119:0.838090:0.666847:0.838090:0.000000
d:@0.666048:0.868982:0.673631:0.868982:0.673631:0.855596:0.666048:0.855596:0.000000
n:@0.546715:0.855932:0.550897:0.855932:0.550897:0.848737:0.546715:0.848737:0.000000
n:@0.609189:0.855932:0.613370:0.855932:0.613370:0.848737:0.609189:0.848737:0.000000
n:@0.655227:0.855932:0.659409:0.855932:0.659409:0.848737:0.655227:0.848737:0.000000
÷:@0.569378:0.860093:0.577655:0.860093:0.577655:0.847352:0.569378:0.847352:0.000000
=:@0.595808:0.860093:0.604086:0.860093:0.604086:0.847352:0.595808:0.847352:0.000000
÷:@0.638265:0.860093:0.646543:0.860093:0.646543:0.847352:0.638265:0.847352:0.000000
Ejemplos:@0.111603:0.918429:0.180154:0.918429:0.180154:0.902851:0.111603:0.902851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.248129:0.908198:0.255487:0.908198:0.255487:0.895377:0.248129:0.895377:0.000000
3:@0.248129:0.925601:0.255487:0.925601:0.255487:0.912780:0.248129:0.912780:0.000000
3:@0.237764:0.912689:0.241719:0.912689:0.241719:0.905798:0.237764:0.905798:0.000000
2:@0.266598:0.897625:0.270553:0.897625:0.270553:0.890734:0.266598:0.890734:0.000000
=:@0.274844:0.916676:0.283121:0.916676:0.283121:0.901932:0.274844:0.901932:0.000000
5:@0.298636:0.908201:0.305993:0.908201:0.305993:0.895380:0.298636:0.895380:0.000000
2:@0.305895:0.901303:0.309849:0.901303:0.309849:0.894412:0.305895:0.894412:0.000000
3:@0.298637:0.925596:0.305995:0.925596:0.305995:0.912775:0.298637:0.912775:0.000000
2:@0.305895:0.918700:0.309849:0.918700:0.309849:0.911809:0.305895:0.911809:0.000000
3:@0.288273:0.912017:0.292227:0.912017:0.292227:0.905126:0.288273:0.905126:0.000000
×:@0.473053:0.918819:0.482158:0.918819:0.482158:0.904804:0.473053:0.904804:0.000000
×:@0.386737:0.918481:0.395014:0.918481:0.395014:0.905740:0.386737:0.905740:0.000000
=:@0.424761:0.918481:0.433039:0.918481:0.433039:0.905740:0.424761:0.905740:0.000000
8:@0.371614:0.909870:0.378972:0.909870:0.378972:0.897049:0.371614:0.897049:0.000000
64:@0.367981:0.927375:0.382545:0.927375:0.382545:0.914554:0.367981:0.914554:0.000000:0.000000
27:@0.401708:0.909870:0.416273:0.909870:0.416273:0.897049:0.401708:0.897049:0.000000:0.000000
125:@0.397939:0.927375:0.419710:0.927375:0.419710:0.914554:0.397939:0.914554:0.000000:0.000000:0.000000
8:@0.452594:0.909870:0.459951:0.909870:0.459951:0.897049:0.452594:0.897049:0.000000
64:@0.448960:0.927375:0.463525:0.927375:0.463525:0.914554:0.448960:0.914554:0.000000:0.000000
27:@0.504127:0.909870:0.518692:0.909870:0.518692:0.897049:0.504127:0.897049:0.000000:0.000000
125:@0.500358:0.927375:0.522129:0.927375:0.522129:0.914554:0.500358:0.914554:0.000000:0.000000:0.000000
3:@0.357241:0.914320:0.361195:0.914320:0.361195:0.907428:0.357241:0.907428:0.000000
3:@0.438232:0.914320:0.442187:0.914320:0.442187:0.907428:0.438232:0.907428:0.000000
3:@0.490908:0.914320:0.494862:0.914320:0.494862:0.907428:0.490908:0.907428:0.000000
9:@0.556939:0.909863:0.564297:0.909863:0.564297:0.897043:0.556939:0.897043:0.000000
4:@0.557075:0.927369:0.564433:0.927369:0.564433:0.914548:0.557075:0.914548:0.000000
16:@0.580264:0.909863:0.594828:0.909863:0.594828:0.897043:0.580264:0.897043:0.000000:0.000000
25:@0.581063:0.927369:0.595627:0.927369:0.595627:0.914548:0.581063:0.914548:0.000000:0.000000
9:@0.625028:0.909863:0.632385:0.909863:0.632385:0.897043:0.625028:0.897043:0.000000
4:@0.625163:0.927369:0.632521:0.927369:0.632521:0.914548:0.625163:0.914548:0.000000
16:@0.661726:0.909863:0.676290:0.909863:0.676290:0.897043:0.661726:0.897043:0.000000:0.000000
25:@0.662525:0.927369:0.677089:0.927369:0.677089:0.914548:0.662525:0.914548:0.000000:0.000000
÷:@0.638309:0.918819:0.647414:0.918819:0.647414:0.904804:0.638309:0.904804:0.000000
÷:@0.568907:0.918481:0.577185:0.918481:0.577185:0.905740:0.568907:0.905740:0.000000
=:@0.600660:0.918481:0.608937:0.918481:0.608937:0.905740:0.600660:0.905740:0.000000
La raíz enésima de un número racional es otro número racional en el que se verifica que::@0.114629:0.764040:0.673490:0.764040:0.673490:0.749795:0.114629:0.749795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.274650:0.782848:0.283919:0.782848:0.283919:0.766487:0.274650:0.766487:0.000000
b:@0.274447:0.802294:0.283716:0.802294:0.283716:0.785933:0.274447:0.785933:0.000000
c:@0.306437:0.782848:0.314103:0.782848:0.314103:0.766487:0.306437:0.766487:0.000000
d:@0.305442:0.802294:0.314711:0.802294:0.314711:0.785933:0.305442:0.785933:0.000000
n:@0.262243:0.787799:0.267754:0.787799:0.267754:0.778317:0.262243:0.778317:0.000000
=:@0.290198:0.792484:0.300314:0.792484:0.300314:0.776911:0.290198:0.776911:0.000000
si y solo si :@0.321347:0.791492:0.390518:0.791492:0.390518:0.777247:0.321347:0.777247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c:@0.403757:0.781873:0.410726:0.781873:0.410726:0.767879:0.403757:0.767879:0.000000
d:@0.402869:0.801210:0.411296:0.801210:0.411296:0.787216:0.402869:0.787216:0.000000
n:@0.423860:0.773110:0.428506:0.773110:0.428506:0.765589:0.423860:0.765589:0.000000
=:@0.433178:0.791292:0.442375:0.791292:0.442375:0.774910:0.433178:0.774910:0.000000
a:@0.447467:0.781875:0.455894:0.781875:0.455894:0.767881:0.447467:0.767881:0.000000
b:@0.447250:0.801213:0.455676:0.801213:0.455676:0.787219:0.447250:0.787219:0.000000
, con n > 1:@0.462551:0.791492:0.532643:0.791492:0.532643:0.777247:0.462551:0.777247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si el índice del radical es :@0.732850:0.784262:0.897459:0.784262:0.897459:0.770016:0.732850:0.770016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
impar, se puede hallar :@0.732850:0.799349:0.882817:0.799349:0.882817:0.785104:0.732850:0.785104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la raíz de un racional :@0.732850:0.814437:0.872833:0.814437:0.872833:0.800192:0.732850:0.800192:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
negativo. Si el índice :@0.732850:0.829524:0.872648:0.829524:0.872648:0.815279:0.732850:0.815279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es par, solo es posible :@0.732850:0.844612:0.880353:0.844612:0.880353:0.830367:0.732850:0.830367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hallar las raíces de :@0.732850:0.859700:0.856298:0.859700:0.856298:0.845454:0.732850:0.845454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
racionales positivos.:@0.732850:0.874787:0.865393:0.874787:0.865393:0.860542:0.732850:0.860542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.762902:0.759235:0.884983:0.759235:0.884983:0.742334:0.762902:0.742334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000