To calculate: To convert the radical expression 324 to rational exponent form and simplify.

Given: 324 Calculation: According to exponential rules, an=a1n Applying the above rule: where a=32,n=4 324=(32)14 According to the power rule, (am)n=amn Applying the above rule: where a=3.m=2,n=14 324=3(2)(14) 324=312

Solved: "To calculate: To convert the radical expression 324..."

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Jason Farmer

Answered question

2021-11-07

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

Answer & Explanation

Clara Reese

Skilled2021-11-08Added 120 answers

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

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