Solve this

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).

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