Question

(125)^–1/3 = ?
(a) 5
(b) –5
(c) $\frac{1}{5}$
(d) $\frac{-1}{5}$

Answer 1

Given $\left(125\right)-\frac{1}{3}=(5^3{)}^{(-\frac{1}{3})}$
$=5^{3\times -\frac{1}{3}}$ [ Since, $(x^a{)}^b=x^{ab}$]
$=5^{-1}=\frac{1}{5}$ [Since, $x^{-a}=\frac{1}{x^a}$]
Hence, the correct answer is option (c).