Question

Which expression is equivalent to (startfraction x superscript negative 4 baseline y over x superscript negative 9 baseline y superscript 5 baseline endfraction) superscript negative 2? assume x not-equals 0, y not-equals 0.

Answer 1

The equivalent expression of $(\frac{x^{-4}y}{x^{-9}y^5})^{-2}$ is $x^{-10}y^8$

Complete question

Which expression is equivalent to $(\frac{x^{-4}y}{x^{-9}y^5})^{-2}$

How to determine the equivalent expression?

The expression is given as:

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

Apply the exponent law of indices

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

Next, we apply the common base law of indices

$(x^{4 -9}y^{5-1})^2$

Evaluate the difference

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

Remove bracket

$x^{-10}y^8$

Hence, the equivalent expression of $(\frac{x^{-4}y}{x^{-9}y^5})^{-2}$ is $x^{-10}y^8$

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