Question:
$(125)^{-1 / 3}=?$
(a) 5
(b) $-5$
(C) $\frac{1}{5}$
(d) $-\frac{1}{5}$
Solution:
$(125)^{-\frac{1}{3}}$
$=\left(5^{3}\right)^{-\frac{1}{3}}$
$=5^{3 \times\left(-\frac{1}{3}\right)} \quad\left[\left(x^{a}\right)^{b}=x^{a b}\right]$
$=5^{-1}$
$=\frac{1}{5} \quad\left(x^{-a}=\frac{1}{x^{a}}\right)$
Hence, the correct answer is option (c).