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 = $( \frac{x^{-4} y}{x^{-9} y^{5} } )^{-2} \\ \\ Distribute\ the \ outer \ exponent \\ \\ = \frac{x^{8} y^{-2} }{x^{18} y^{-10} } \\ \\ factor \ by \ subtracting \ exponents \\ \\ = \frac{y^{8} }{ x^{10} }$

Answer 2

Answer:

$\frac{y^8}{x^{10}}$

Step-by-step explanation:

The given expression is

$(\frac{x^{-4}y}{x^{-9}y^5})^{-2}$

Distribute -2 inside the parenthesis

multiply -2 with each exponent

$(\frac{x^{8}y^{-2}}{x^{18}y^{-10}})$

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

$\frac{x^{-10}y^8}{1}$

write the answer with positive exponent

$\frac{y^8}{x^{10}}$