single powers of 4

**andyboy179** · January 30th 2010, 11:08 AM

hi this is my question:
write in single power of 4
(4^2)^3

how would i do this?

**VonNemo19** · January 30th 2010, 11:13 AM

Originally Posted by andyboy179

hi this is my question:
write in single power of 4
(4^2)^3

how would i do this?

Note that $(4^2)^3=(4\cdot4)^3=(4\cdot4)(4\cdot4)(4\cdot4)=4\ cdot4\cdot4\cdot4\cdot4\cdot4=?$

**andyboy179** · January 30th 2010, 11:22 AM

=4096?

**VonNemo19** · January 30th 2010, 11:26 AM

Originally Posted by andyboy179

=4096?

Well, yeah....but the problem asked for $(4^2)^3=4^{x}$ . So, from looking at my above post, what number should replace the $x$ here?

**andyboy179** · January 30th 2010, 11:29 AM

3?

**VonNemo19** · January 30th 2010, 11:34 AM

Originally Posted by andyboy179

3?

Not quite. My first post says that $(4^2)^3$ is the same thing as $4\cdot4\cdot4\cdot4\cdot4\cdot4$ which is the same thing as $4^{\color{red}6}$ .

So, the answer is $(4^2)^3=4^6$ .

And moreover, in general, $(a^m)^n=a^{m\cdot{n}}$

**andyboy179** · January 30th 2010, 11:39 AM

Originally Posted by VonNemo19

Not quite. My first post says that $(4^2)^3$ is the same thing as $4\cdot4\cdot4\cdot4\cdot4\cdot4$ which is the same thing as $4^{\color{red}6}$ .

So, the answer is $(4^2)^3=4^6$ .

And moreover, in general, $(a^m)^n=a^{m\cdot{n}}$

oh so i times to 2 top numbers? so is the question was (4^3)^5 it would = 4^15?

**VonNemo19** · January 30th 2010, 11:44 AM

Originally Posted by andyboy179

oh so i times to 2 top numbers? so is the question was (4^3)^5 it would = 4^15?

Ideed.

**andyboy179** · January 30th 2010, 11:46 AM

cheers mate! if it was (4^3)^-2 i would do the same so it would be 4^-6

**VonNemo19** · January 30th 2010, 11:55 AM

Originally Posted by andyboy179

cheers mate! if it was (4^3)^-2 i would do the same so it would be 4^-6

Correct.

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