could someone tell me how to set this up step by step. this is a sample of a question on a test. I seen how by classmates kind of did it but it doesn't make sense to me. 
Nathan B. answered • 01/17/20
Elementary and Algebraic skilled
I'm not exactly sure what you mean by "set this up," as there is no listed problem to solve, so all I can tell you is what's going on.
Think of it as you're dividing exponents here, and the root sign acts as the parentheses. You distribute that 3 into the denominator of each part that gets multiplied. Example:
√(25x2) → 25^1/2 * x^2/2 = 5x
√(25 + x2) → (25 + x2)^1/2
So what's happening in your problems case is that you would distribute that 1/3 exponent to each part, as each part is multiplying, like in that example:
5000^1/3 * x^12/3 * y^13/3 z^2/3
The joys of a text box, right?
Anyways, the only exponent that divides cleanly would be the x12. 12 divided by 3 equals 4, so x4 can be set outside of the root:
x4 3√(5000y13z2)
I mean, you could have y to the thirteen-thirds and z to the two-thirds outside of the root technically, but that just looks ugly.
