Vorbeckenuc

2022-07-26

Simplify the following expression. Assume that all variables represent positive real numbers.
$\left(\frac{{x}^{-4}}{{y}^{3}}{\right)}^{-4}$

Rihanna Robles

Expert

$\left(\frac{{x}^{-4}}{{y}^{3}}{\right)}^{-4}$
We have a property $\left(\frac{x}{y}{\right)}^{-a}=\left(\frac{y}{x}{\right)}^{a}$
so, we have
$\left(\frac{{y}^{3}}{{x}^{-4}}{\right)}^{4}\phantom{\rule{0ex}{0ex}}=\left({y}^{3}\cdot \frac{1}{x-4}{\right)}^{4}\phantom{\rule{0ex}{0ex}}=\left({y}^{3}{x}^{4}{\right)}^{4}\phantom{\rule{0ex}{0ex}}={y}^{3\cdot 4}\cdot {x}^{4\cdot 4}\phantom{\rule{0ex}{0ex}}={y}^{12}{x}^{16}$

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