# To calculate:To convert the radical expression \sqrt[4]{3^{2}} to rat

Jason Farmer 2021-11-07 Answered

To calculate:
To convert the radical expression $\sqrt[4]{{3}^{2}}$ to rational exponent form and simplify.

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## Expert Answer

Clara Reese
Answered 2021-11-08 Author has 120 answers

Given: $\sqrt[4]{{3}^{2}}$
Calculation:
According to exponential rules, $\sqrt[n]{a}={a}^{\frac{1}{n}}$
Applying the above rule: where $a={3}^{2},n=4$
$\sqrt[4]{{3}^{2}}=\left({3}^{2}{\right)}^{\frac{1}{4}}$
According to the power rule, ${\left({a}^{m}\right)}^{n}={a}^{mn}$
Applying the above rule: where $a=3.m=2,n=\frac{1}{4}$
$\sqrt[4]{{3}^{2}}={3}^{\left(2\right)\left(\frac{1}{4}\right)}$
$\sqrt[4]{{3}^{2}}={3}^{\frac{1}{2}}$

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