Simplify:
$ \left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4} $

Given:

\( \left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4} \)

To do:

We have to simplify \( \left(\frac{5}{8}\right)^{-7} \times\left(\frac{8}{5}\right)^{-4} \).

Solution:
We know that,

$a^{-m}=\frac{1}{a^m}$

Therefore,

$(\frac{5}{8})^{-7} \times (\frac{8}{5})^{-4}=(\frac{8}{5})^7 \times (\frac{5}{8})^4$

$=\frac{8^7\times5^4}{5^7\times8^4}$

$=8^{7-4}\times5^{4-7}$

$=8^{3}\times5^{-3}$

$=\frac{8^3}{5^3}$

$=(\frac{8}{5})^3$

Hence, $(\frac{5}{8})^{-7} \times (\frac{8}{5})^{-4}=(\frac{8}{5})^3$.

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Updated on: 10-Oct-2022

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