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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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