The value of (-1/216)-2/3 is · ABC26GN1908
Subject: General Aptitude · Chapter: Surds and Indices
The value of $\left(-\frac{1}{216}\right)^{-\frac{2}{3}}$ is
(a)36
(b)- 36
(c)$\frac{1}{36}$
(d)$-\frac{1}{36}$
Answer
Explanation
$\left(-\frac{1}{216}\right)^{-\frac{2}{3}}=\left[\left(-\frac{1}{6}\right)^{3}\right]^{-\frac{2}{3}}=\left(-\frac{1}{6}\right)^{3 \times \frac{(-2)}{3}}$ $$=\left(-\frac{1}{6}\right)^{-2}=\frac{1}{\left(-\frac{1}{6}\right)^{2}}=\frac{1}{\left(\frac{1}{36}\right)}=36 .$$
Explanation as extracted from the printed page; notation may be imperfect.
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