How do you simplify ${(5^{\frac{2}{3}})}^{\frac{1}{2}}$ $(5^(2/3))^(1/2)$ ?

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Answer 1 · 2018-08-08T01:59:07

$\sqrt[3]{5}$ $root3(5)$

When we take a power to a power, we multiply the powers. We now have

$5^{\frac{2}{3} \cdot \frac{1}{2}} = 5^{\frac{2}{6}} = 5^{\frac{1}{3}} = \sqrt[3]{5}$ $5^(2/3*1/2)=5^(2/6)=5^(1/3)=root3(5)$

Hope this helps!

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