# Thread: single powers of 4

1. ## single powers of 4

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

how would i do this?

2. 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 $\displaystyle (4^2)^3=(4\cdot4)^3=(4\cdot4)(4\cdot4)(4\cdot4)=4\ cdot4\cdot4\cdot4\cdot4\cdot4=?$

3. =4096?

4. Originally Posted by andyboy179
=4096?
Well, yeah....but the problem asked for $\displaystyle (4^2)^3=4^{x}$. So, from looking at my above post, what number should replace the $\displaystyle x$ here?

5. 3?

6. Originally Posted by andyboy179
3?
Not quite. My first post says that $\displaystyle (4^2)^3$ is the same thing as $\displaystyle 4\cdot4\cdot4\cdot4\cdot4\cdot4$ which is the same thing as $\displaystyle 4^{\color{red}6}$.

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

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

7. Originally Posted by VonNemo19
Not quite. My first post says that $\displaystyle (4^2)^3$ is the same thing as $\displaystyle 4\cdot4\cdot4\cdot4\cdot4\cdot4$ which is the same thing as $\displaystyle 4^{\color{red}6}$.

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

And moreover, in general, $\displaystyle (a^m)^n=a^{m\cdot{n}}$
oh so i times to 2 top numbers? so is the question was (4^3)^5 it would = 4^15?

8. 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.

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

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