Question

9. Given x>0x>0 and y>0,y>0, select the expression that is equivalent to

Answer 1

Solution

Given

$\sqrt[3]{27x^5y^8}$

Using the laws of indices

$\sqrt[3]{27x^5y^8}=(27x^5y^8)^{\frac{1}{3}}=27^{\frac{1}{3}}\times x^{5\times\frac{1}{3}}\times y^{\frac{8}{3}}$

$\begin{gathered} \text{ since }27^{\frac{1}{3}}=3 \\ \\ \Rightarrow27^{\frac{1}{3}}\times x^{\frac{5}{3}}\times y^{\frac{8}{3}}=3x^{\frac{5}{3}}y^{\frac{8}{3}} \end{gathered}$