How to solve rational exponents with vairables in fraction.?

Question

I am trying some homework here and there is an equation that i need to simplify.

8x^9 y^3
______
27x^2 y^12 all to the 2/3 power.. please help.. im lost here!

Answer 1

First perform the divisions of each term, constant, x and y:

8/27 (cannot be reduced)

x^9/x^2 = x^7 (subtract exponents)

y^3/y^12 = y^-9

This leaves [(8/27)*(x^2)*(y^-9)]^(2/3)

Now multiply exponents of the terms by 2/3

(8/27)^2/3 * x^(4/3) * y^-6

(8/27)^(2/3) = (2/3)^2 = 4/9

put it all together: 4*x^(4/3) / 9^y^6