Question

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

Answer 1

Given

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

Using the laws of indices

`\sqrt[3]{27x^5y^8}=(27x^5y^8)^{(1)/(3)}=27^{(1)/(3)}* x^{5*(1)/(3)}* y^{(8)/(3)}`

`\begin{gathered} \text{ since }27^{(1)/(3)}=3 \\ \\ \Rightarrow27^{(1)/(3)}* x^{(5)/(3)}* y^{(8)/(3)}=3x^{(5)/(3)}y^{(8)/(3)} \end{gathered}`