Question

Simplify:

$\left(vi\right)$ $(125x^{-3}{)}^{\frac{1}{3}}$

Answer 1

Simplify the given expression

$(125x^{-3}{)}^{\frac{1}{3}}$

$=(5^3{)}^{\frac{1}{3}}\times (x^{-3}{)}^{\frac{1}{3}}$ $[\because (ab{)}^m=a^m{b}^m]$

$=(5{)}^{3\times \frac{1}{3}}\times (x{)}^{-3\times \frac{1}{3}}$ $[\because (a^m{)}^n=a^{mn}]$

$=5x^{-1}$ $[\because \frac{1}{a^m}=a^{-m}]$
$=\frac{5}{x}$
Hence, $\left(125x^{-3}\right)\frac{1}{3}=5x^{-1}or\frac{5}{x}$.