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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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