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

asked Aug 1, 2023 98.6k views

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3 votes

Solution

Given

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

Using the laws of indices

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

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

Yuval Peled answered Aug 5, 2023

6.9k points

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