Simplify:
$ \left(-\frac{3}{8}\right)^{-3} \div\left(\frac{9}{4}\right)^{-3} $

Given:

\( \left(-\frac{3}{8}\right)^{-3} \div\left(\frac{9}{4}\right)^{-3} \)

To do:

We have to simplify \( \left(-\frac{3}{8}\right)^{-3} \div\left(\frac{9}{4}\right)^{-3} \).

Solution:
We know that,

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

Therefore,

$(-\frac{3}{8})^{-3} \div (\frac{9}{4})^{-3}=(-\frac{8}{3})^3 \div (\frac{4}{9})^3$

$=(-\frac{8}{3})^3 \times (\frac{9}{4})^3$

$=\frac{-8^3\times9^3}{3^3\times4^3}$

$=\frac{-4^3\times2^3\times3^3\times3^3}{3^3\times4^3}$

$=-2^3\times3^3$

$=-8\times27$

$=-216$

Hence, $(-\frac{3}{8})^{-3} \div (\frac{9}{4})^{-3}=-216$.

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Updated on: 10-Oct-2022

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