Question
Simplify: $\frac{8^{\frac{1}{3}}\times16^{\frac{1}{3}}}{32^{-\frac{1}{3}}}$
✓
Answer
$\frac{8^{\frac{1}{3}}\times16^{\frac{1}{3}}}{32^{-\frac{1}{3}}}=\frac{(2^3)^{\frac{1}{3}}\times(2^4)^{\frac{1}{3}}}{(2^5)^{-\frac{1}{3}}}=\frac{2^{3\times\frac{1}{3}}\times2^{4\times\frac{1}{3}}}{2^{5\times-\frac{1}{3}}}$ $[\because(\text{a}^\text{m})^\text{n}=\text{a}^\text{mn}]$ $\frac{2^{\frac{3}{3}+\frac{4}{3}}}{2^{-\frac{5}{3}}}=\frac{2^{\frac{7}{3}}}{2^{-\frac{5}{3}}}=2^{\frac{7}{3}+\frac{5}{3}}=2^{\frac{12}{3}}=2^4=16$ $\Big[\because\frac{\text{a}^\text{m}}{\text{a}^\text{n}}=\text{a}^{\text{m}-\text{n}}\Big]$
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