Question

Simplify: ${64}^{-\frac{1}{3}}[{64}^{\frac{2}{3}}+{64}^{\frac{1}{3}}]$

Answer 1

${64}^{-\frac{1}{3}}[{64}^{\frac{1}{3}}+{64}^{\frac{2}{3}}]$

$={64}^{-\frac{1}{3}}\times {64}^{\frac{1}{3}}+{64}^{-\frac{1}{3}}\times {64}^{\frac{2}{3}}$

$={64}^{(-\frac{1}{3}+\frac{1}{3})}+{64}^{(-\frac{1}{3}+\frac{2}{3})}$

$=1+{64}^{\frac{1}{3}}$

$=1+\sqrt[3]{364}$

$=1+4$

$=5$