# single powers of 4

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• Jan 30th 2010, 11:08 AM
andyboy179
single powers of 4
hi this is my question:
write in single power of 4
(4^2)^3

how would i do this?
• Jan 30th 2010, 11:13 AM
VonNemo19
Quote:

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 $(4^2)^3=(4\cdot4)^3=(4\cdot4)(4\cdot4)(4\cdot4)=4\ cdot4\cdot4\cdot4\cdot4\cdot4=?$
• Jan 30th 2010, 11:22 AM
andyboy179
=4096?
• Jan 30th 2010, 11:26 AM
VonNemo19
Quote:

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?
• Jan 30th 2010, 11:29 AM
andyboy179
3?
• Jan 30th 2010, 11:34 AM
VonNemo19
Quote:

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, $(a^m)^n=a^{m\cdot{n}}$
• Jan 30th 2010, 11:39 AM
andyboy179
Quote:

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?
• Jan 30th 2010, 11:44 AM
VonNemo19
Quote:

Originally Posted by andyboy179
oh so i times to 2 top numbers? so is the question was (4^3)^5 it would = 4^15?

(Yes) Ideed. (Wink)
• Jan 30th 2010, 11:46 AM
andyboy179
cheers mate! if it was (4^3)^-2 i would do the same so it would be 4^-6
• Jan 30th 2010, 11:55 AM
VonNemo19
Quote:

Originally Posted by andyboy179
cheers mate! if it was (4^3)^-2 i would do the same so it would be 4^-6

Correct.