Respuesta :

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(x^-4y/x^-9y^5)^-2 = [tex]( \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} } [/tex]

Answer:

[tex]\frac{y^8}{x^{10}}[/tex]

Step-by-step explanation:

The given expression is

[tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]

Distribute -2 inside the parenthesis

multiply -2 with each exponent

[tex](\frac{x^{8}y^{-2}}{x^{18}y^{-10}})[/tex]

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

[tex]\frac{x^{-10}y^8}{1}[/tex]

write the answer with positive exponent

[tex]\frac{y^8}{x^{10}}[/tex]

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