simplify (-32a^10)^(3/5)

Question

anonymous · Answer

First, it's important to recognize that 32 and $a^{10}$ are 5th powers.  So, taking fifth roots, we get $(-2a^{2})^{3}$.  Are you good from here?

smurfy14 · Answer

no. what do you mean 5th roots??

anonymous · Answer

So 5th roots are kind of like square roots

anonymous · Answer

4 is the square of 2, so $\sqrt{4}=2$.

anonymous · Answer

$2^{5}=32$, so $32^{1/5}=2$.

smurfy14 · Answer

ok and you get a^2 by dividing 10 by 5 right?...so what happened to the denominator of five outside the ()?

anonymous · Answer

That goes away because we divided the powers by 5.

smurfy14 · Answer

...ok so is that the final answer?

anonymous · Answer

Well no, now you still have to cube it.

smurfy14 · Answer

-8a^6 correct?

anonymous · Answer

Perfect.

smurfy14 · Answer

ok cool so how would you do (9^(1/2)+16^(1/2))^-2?

anonymous · Answer

Ick, that's an ugly one. Are you sure there is a plus in there?

smurfy14 · Answer

haha ya

anonymous · Answer

Stupid me, it's way easy, 9 and 16 are squares.

smurfy14 · Answer

oh ok i see it :P do you know what 7^-2 would be?

anonymous · Answer

$$\frac{1}{7^{2}}$$, right?, which then becomes? (leave it in a fraction)

smurfy14 · Answer

oh ok! if you dont mind could you help me with like four more? i have this as a precalc summer assignment and we havent learned any of this yet.

anonymous · Answer

Actually, I can't sorry, I have to take off.  I am tutoring someone at 5.

smurfy14 · Answer

ok well thanks for the help!

anonymous · Answer

You're very welcome, sorry I couldn't help you on the other four.

smurfy14 · Answer

its fine.