Question
Simplify:
$\frac{1}{27}^{\frac{-2}{3}}$
$\frac{1}{27}^{\frac{-2}{3}}$
✓
Answer
$\Big(\frac{1}{27}\Big)^{\frac{-2}{3}}=\Big(\frac{1}{3^3}\Big)^{\frac{-2}{3}}=(3^{-3})^{-\frac{2}{3}}$ $\Big[\because\frac{1}{\text{a}}=\text{a}^{-1}\Big]$
$=3^{-3\times-\frac{2}{3}}=3^2=9$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$
$=3^{-3\times-\frac{2}{3}}=3^2=9$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$
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