Question

How do you simplify `(x^-4)^5(x^3y^2)^5`?

Answer 1

`x^{-5}y^{10}`

Explanation:

First rule to use: the power of powers means to multiply the exponents, so

1. `(x^{-4})^5 = x^{-4*5} = x^{-20}`
2. `(x^3y^2)^5 = x^{3*5}y^{2*5} = x^{15}y^{10}`

So, your expression becomes

`x^{-20}*x^{15}y^{10}`

Second rule to use: the product of powers with the same base means to sum the exponents. So, the `y` power is alone and we'll leave it untouched. As for the `x` powers, we have

`x^{-20}*x^{15} = x^{-20+15}=x^{-5}`.