Algebra Examples

${(\sqrt[4]{144})}^{2}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{144}$ as $144^{\frac{1}{4}}$ .

${(144^{\frac{1}{4}})}^{2}$

Step 2

Multiply the exponents in ${(144^{\frac{1}{4}})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$144^{\frac{1}{4} \cdot 2}$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$144^{\frac{1}{2 (2)} \cdot 2}$

Cancel the common factor.

$144^{\frac{1}{2 \cdot 2} \cdot 2}$

Rewrite the expression.

$144^{\frac{1}{2}}$