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$ \quad $ Simplify $ \left(3^{3}-2^{3}\right) \times\left(\frac{2}{3}\right)^{-3} $
$\left(3^{3}-2^{3}\right)\left(\frac{2}{3}\right)^{-3}$
Apply exponent rule: $a^{-b}=\frac{1}{a^{b}}$
$=\frac{1}{\left(\frac{2}{3}\right)^{3}}\left(3^{3}-2^{3}\right)$
$\frac{1}{\left(\frac{2}{3}\right)^{3}}=\frac{3^{3}}{2^{3}}$
$=\frac{3^{3}}{2^{3}}\left(3^{3}-2^{3}\right)$
Multiply fractions: $\quad a \times \frac{b}{c}=\frac{a \times b}{c}$
$=\frac{3^{3}\left(3^{3}-2^{3}\right)}{2^{3}}$
$3^{3\left(3^{3}-2^{3}\right)}=3^{3} \times 19$
$=\frac{3^{3} \times 19}{2^{3}}$
$3^{3} \times 19=513$
$=\frac{513}{2^{3}}$
$2^{3}=8$
$=\frac{513}{8}$
Updated on: 10-Oct-2022
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