Simplify the expression and eliminate any negative exponents(s). Assume that all

Question

Simplify the expression and eliminate any negative exponents(s). Assume that all

glamrockqueen7 2021-10-26 Answered

Simplify the expression and eliminate any negative exponents(s). Assume that all letters denote positive numbers.
$\sqrt[6]{y^{5}} \sqrt[3]{y^{2}}$

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Expert Answer

falhiblesw

Answered 2021-10-27 Author has 97 answers

The given expression is, $\sqrt[6]{y^{5}} \sqrt[3]{y^{2}}$
Simplify the expression using the laws of exponents as follows.
$\sqrt[6]{y^{5}} \sqrt[3]{y^{2}} = {(y^{5})}^{\frac{1}{6}} {(y^{2})}^{\frac{1}{3}}$
$= y^{\frac{5}{6}} y^{\frac{2}{3}}$
$= y^{\frac{5}{6} + \frac{2}{3}}$
$= y^{\frac{5 + 4}{6}}$
$= y^{\frac{9}{6}}$
$= y^{\frac{3}{2}}$
Thus, the simplified answer is $y^{\frac{3}{2}}$

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