Question

Simplify :

$\frac{8^{\frac{1}{3}}\times {16}^{\frac{1}{3}}}{{32}^{-\frac{1}{3}}}$

Answer 1

$\frac{8^{\frac{1}{3}}\times {16}^{\frac{1}{3}}}{{32}^{-\frac{1}{3}}}$

$=\frac{{\left[\left(2^3\right)\right]}^{\frac{1}{3}}\times {\left[\left(2^4\right)\right]}^{\frac{1}{3}}}{{\left[\left(2^5\right)\right]}^{\frac{-1}{3}}}$

$=\frac{2^{\frac{3}{3}}\times 2^{\frac{4}{3}}}{2^{\frac{-5}{3}}}$

$=2^1\times 2^{\frac{4}{3}}\times 2^{\frac{5}{3}}$

$=2^{1+\frac{4}{3}+\frac{5}{3}}$

$=2^{\frac{3+4+5}{3}}$

$=2^{\frac{12}{3}}$

$=2^4$

$=16$