Algebra Examples

${(\sqrt{9 x^{8} y^{2}})}^{\frac{1}{2}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{9 x^{8} y^{2}}$ as ${(9 x^{8} y^{2})}^{\frac{1}{2}}$ .

${({(9 x^{8} y^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$

Step 2

Multiply the exponents in ${({(9 x^{8} y^{2})}^{\frac{1}{2}})}^{\frac{1}{2}}$ .

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Step 2.1

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

${(9 x^{8} y^{2})}^{\frac{1}{2} \cdot \frac{1}{2}}$

Step 2.2

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

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Step 2.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

${(9 x^{8} y^{2})}^{\frac{1}{2 \cdot 2}}$

Step 2.2.2

Multiply $2$ by $2$ .

${(9 x^{8} y^{2})}^{\frac{1}{4}}$