Question

Complete the puzzle by clicking on the puzzle piece that contains equivalent expression.

Answer 1

-5 when ...

Explanation:

The rules of exponents can help you simplify the given product.

Rules

(a/b)^c = (a^c)/(b^c)

(ab)^c = (a^c)(b^c)

(a^b)(a^c) = a^(b+c)

(a^b)/(a^c) = a^(b-c)

Application

`\left((x)/(y)\right)^2(-x^2y)^3=\\\\(x^2(-1)^3(x^2)^3y^3)/(y^2)=-x^(2+2\cdot3)y^(3-2)=-x^8y`

This expression does not match any of those offered.

When x=-1 and y=5, this becomes ...

`-(-1)^8(5)=\boxed{-5}`