By what number should $(-\frac{2}{3})^{-5}$ be divided to get $( -\frac{2}{3})^{4}$?

Given: Fraction $(-\frac{2}{3})^{-5}$.

To do: To find the number which should $(-\frac{2}{3})^{-5}$ be divided to get $( -\frac{2}{3})^{4}$?

Solution: 

Let $x$ be the number.

Therefore, $(-\frac{2}{3})^{-5}\div x=( -\frac{2}{3})^{4}$

$\Rightarrow x=\frac{(-\frac{2}{3})^{-5}}{( -\frac{2}{3})^{4}}$

$\Rightarrow x=(-\frac{2}{3})^{-5-4}$

$\Rightarrow x=(-\frac{2}{3})^{-9}$

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Updated on: 10-Oct-2022

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