Question

Which expression is equivalent to (x^-4y/x^-9y^5)^-2 ? Assume x ≠ 0, y ≠ 0

Answer 1

(x^-4y/x^-9y^5)^-2 =
`( (x^(-4) y)/(x^(-9) y^(5) ) )^(-2) \\ \\ Distribute\ the \ outer \ exponent \\ \\ = (x^(8) y^(-2) )/(x^(18) y^(-10) ) \\ \\ factor \ by \ subtracting \ exponents \\ \\ = (y^(8) )/( x^(10) )`

Answer 2

`(y^8)/(x^(10))`

Explanation:

The given expression is

`((x^(-4)y)/(x^(-9)y^5))^(-2)`

Distribute -2 inside the parenthesis

multiply -2 with each exponent

`((x^(8)y^(-2))/(x^(18)y^(-10)))`

Simplify it further

a^m/a^n= a^m-n

x^8/x^18 = x^-10

y^-2 / y^-10 = y^8

So final answer is

`(x^(-10)y^8)/(1)`

write the answer with positive exponent

`(y^8)/(x^(10))`