Question

The simplified form of ${(-\frac{1}{27})}^{\frac{-2}{3}}$ is

• A. 9
• B. -9
• C. $\frac{1}{9}$
• D. $-\frac{1}{9}$

Answer 1

Answer: (A)

Given ${(-\frac{1}{27})}^{\frac{-2}{3}}={\left[{(-\frac{1}{3})}^3\right]}^{\frac{-2}{3}}$
$={(-\frac{1}{3})}^{3\times \frac{-2}{3}}={(-\frac{1}{3})}^{-2}$ [since,${\left(a^m\right)}^n=a^{(m\times n)}$]
$=(-3{)}^2$ [Since, $[\frac{1}{a}{]}^{-m}=a^m$]
$=(-3)\times (-3)=9$
Hence, the simplified form of the given expression is $=9$.