Question

(4^(12a )/ 5^(12a)) ^1/3
Rewrite the following expression without parentheses. Simplify your answer as much as possible, and assume that all variables are positive

Answer 1

http://www.wolframalpha.com/input/?i=%284%5E%2812a+%29%2F+5%5E%2812a%29%29+%5E1%2F3

Answer 2

\[\Large\rm \left(\frac{4^{12a}}{5^{12a}}\right)^{1/3}\]Hey owl :O
We need to simplify this?

Answer 3

Recall that when we have something like this:
\[\Large\rm (x^2)^3=x^{2\cdot3}=x^6\]Exponent and another exponent outside, we multiply the values.

Answer 4

yeah

Answer 5

To get rid of the brackets, you need to distribute the 1/3 to both the exponential in the top AND bottom.

Answer 6

\[\Large\rm \left(\frac{4^{12a}}{5^{12a}}\right)^{1/3}=\frac{\left(4^{12a}\right)^{1/3}}{\left(5^{12a}\right)^{1/3}}\]

Answer 7

And then multiply the exponents, yah? :o

What's 12 times 1/3?

Answer 8

4

Answer 9

\[\Large\rm =\frac{4^{4a}}{5^{4a}}\]Mmmm ok good good good.
Applying that exponent rule to each the top and bottom gives us something like this, yes?

Answer 10

yup

Answer 11

Since the `bases` of these exponentials are different, there isn't much else we can do with them.

We would stop there :D

Answer 12

ok thank you very much!