# Rational Exponents

I'm just checking to see if have the correct answer because my teacher didn't give us an answer key and i like to know that I have done one question properly before doing the rest.

Evaluate. Express answer as an exact number - No decimals.

$$(3^{\frac 13} \times 5^{-\frac 12})^{6}$$

Here is my work:

$$(3^{\frac 13} \times 5^{-\frac 12})^{6}$$ $$=3^{2} \times 5^{-3}$$ $$=\frac{9\times 1}{125}$$ $$=\frac{9}{125}$$

Now I'm not sure if this is the right answer. For some reason I feel it's wrong.

• You, indeed, have the right solution and your work/method is correct. As a future note, this stack exchange isn't really the right place for these type of questions. Hopefully, an answer will come along soon (but I don't see how it would differ) Commented Mar 31, 2015 at 22:17
• You showed your work, so the question is fine. (And the answer is correct.) Commented Mar 31, 2015 at 22:22
• Actually, these questions are welcomed. Because the answers would be breif, people usually answer in the comments if it is correct, but as a full answer when the work is wrong. It is best to tag these with (proof-verification).
– Teoc
Commented Mar 31, 2015 at 22:25
• @MathNoob I'll remember that for next time! Commented Mar 31, 2015 at 22:27

This is correct. ${}{}{}{}{}{}{}{}$