Question

What is the right answer?

Answer 1

C

Explanation:

Use the exponential rules

• `(x^a)^b=x^(ab)`

• `x^a*x^b=x^(a+b)`

Therefore

`(x^(-2)*y^4)^(1/3)*x^2*y^(-1/3)`

`=(x^(-2))^(1/3)*(y^4)^(1/3)*x^2*y^(-1/3)`

`=x^(-2/3)*y^(4/3)*x^2*y^(-1/3)`

`=(x^(-2/3)*x^2)(y^(4/3)*y^(-1/3))`

`=(x^(-2/3+2))*(y^(4/3-1/3))`

`=x^(4/3)*y`

Answer 2

I will let you do the final part

Explanation:

Given: `color(green)((x^(-2)y^4)^(1/3)x^2y^(-1/3))`

The trick is to take at least some of it one step at a time. Other parts you may be able to jump steps.

If you are unsure about the negative indices do this:

Write as `color(green)( (y^4/x^2)^(1/3) x^2/y^(1/3)`

`color(green)( (y^(4/3)/x^(2/3)) x^2/y^(1/3)`

`color(green)((y^(4/3))/(y^(1/3)) xx x^2/(x^(2/3)))`

`color(green)(y^(4/3-1/3)color(white)(.)x^(2-2/3))`

I will let you finish this off