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2 y 3 - Amolasmates

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3. Calcular las siguientes potencias de base fraccionaria, dejando el resultado en forma fraccionaria:<br />

0,1<br />

2<br />

9<br />

-<br />

2<br />

7<br />

2<br />

5<br />

-<br />

2<br />

3<br />

2<br />

3<br />

7<br />

4<br />

2<br />

5<br />

2<br />

3<br />

2<br />

1<br />

-<br />

2<br />

1<br />

2<br />

1<br />

-<br />

2<br />

1<br />

2<br />

1<br />

3<br />

1<br />

2<br />

1<br />

2<br />

1<br />

2<br />

1<br />

-<br />

5<br />

2<br />

6<br />

5<br />

-<br />

4<br />

9<br />

4<br />

3<br />

-<br />

5<br />

1<br />

-<br />

4<br />

9<br />

3<br />

5<br />

1<br />

3<br />

3<br />

2<br />

2<br />

3<br />

3<br />

2<br />

2<br />

3<br />

3<br />

2<br />

2<br />

3<br />

1<br />

2<br />

2<br />

5<br />

1<br />

2<br />

2<br />

3<br />

2<br />

2<br />

3<br />

- =<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛ −<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛ −<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛ −<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛ −<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

=<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

−<br />

4. Pasar a forma de potencia de base entera lo más simple posible:<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

125<br />

1<br />

1024<br />

1<br />

a<br />

m<br />

i<br />

s<br />

cienmilé<br />

1<br />

a<br />

millonésim<br />

1<br />

milésima<br />

1<br />

trillón<br />

1<br />

billón<br />

1<br />

millón<br />

1<br />

0,001<br />

0,01<br />

0,1<br />

1.000.000<br />

1<br />

10.000<br />

1<br />

100<br />

1<br />

1.000.000<br />

10.000<br />

100<br />

64<br />

1<br />

14<br />

1<br />

10<br />

1<br />

5<br />

1<br />

4<br />

1<br />

3<br />

1<br />

343<br />

125<br />

81<br />

32<br />

8<br />

5. Pasar a potencia única de base racional, y simplificar el resultado:<br />

( )<br />

( ) ( ) ( )<br />

3<br />

3<br />

3<br />

·<br />

3<br />

3<br />

5<br />

:<br />

2<br />

-<br />

2<br />

3<br />

3<br />

2<br />

3<br />

3<br />

2<br />

2<br />

3<br />

2<br />

3<br />

3<br />

2<br />

2<br />

3<br />

2<br />

2<br />

4<br />

5<br />

1<br />

4<br />

5<br />

4<br />

2<br />

5<br />

6<br />

2<br />

5<br />

3<br />

10<br />

7<br />

2<br />

10<br />

7<br />

4<br />

10<br />

7<br />

6<br />

10<br />

7<br />

6<br />

4<br />

7<br />

5<br />

4<br />

7<br />

2<br />

4<br />

7<br />

3<br />

2<br />

3<br />

-<br />

2<br />

3<br />

-<br />

3<br />

0<br />

9<br />

5<br />

-<br />

2<br />

-<br />

6<br />

3<br />

2<br />

-<br />

7<br />

4<br />

10<br />

20<br />

-<br />

10<br />

4<br />

10<br />

20<br />

10<br />

3<br />

9<br />

0<br />

9<br />

5<br />

-<br />

6<br />

2<br />

-<br />

6<br />

3<br />

7<br />

2<br />

-<br />

7<br />

4<br />

-<br />

10<br />

20<br />

-<br />

10<br />

4<br />

10<br />

20<br />

-<br />

10<br />

4<br />

10<br />

20<br />

10<br />

3<br />

9<br />

0<br />

9<br />

5<br />

-<br />

6<br />

2<br />

-<br />

6<br />

3<br />

7<br />

2<br />

-<br />

7<br />

2<br />

(-6)<br />

2<br />

(-7)<br />

3<br />

6)<br />

(<br />

3<br />

7<br />

2<br />

6<br />

2<br />

(-7)<br />

3<br />

6<br />

3<br />

7<br />

2<br />

6<br />

2<br />

7<br />

3<br />

(-6)<br />

3<br />

(-7)<br />

2<br />

(-6)<br />

2<br />

7<br />

3<br />

6<br />

3<br />

(-7)<br />

2<br />

6<br />

2<br />

7<br />

-<br />

3<br />

6<br />

3<br />

7<br />

2<br />

6<br />

2<br />

7<br />

5<br />

-<br />

7<br />

3<br />

2<br />

3<br />

2<br />

4<br />

3<br />

4<br />

3<br />

5<br />

3<br />

5<br />

3<br />

5<br />

5<br />

3<br />

=<br />

−<br />

=<br />

=<br />

−<br />

=<br />

−<br />

⋅<br />

=<br />

−<br />

⋅<br />

=<br />

−<br />

⋅<br />

=<br />

−<br />

=<br />

−<br />

=<br />

=<br />

−<br />

⋅<br />

⋅<br />

−<br />

⋅<br />

−<br />

=<br />

⋅<br />

⋅<br />

=<br />

⋅<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

=<br />

−<br />

=<br />

=<br />

=<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

=<br />

⋅<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

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⎠<br />

⎞<br />

⎜<br />

⎝<br />

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⎠<br />

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⎜<br />

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⎝<br />

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⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

⎟<br />

⎠<br />

⎞<br />

⎜<br />

⎝<br />

⎛<br />

11

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