Algebra Examples

{(\sqrt{7})}^{3}

${(\sqrt{7})}^{3}$

Step 1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{7}

$\sqrt{7}$ as

7^{\frac{1}{2}}

$7^{\frac{1}{2}}$ .

{(7^{\frac{1}{2}})}^{3}

${(7^{\frac{1}{2}})}^{3}$

Step 2

Multiply the exponents in

{(7^{\frac{1}{2}})}^{3}

${(7^{\frac{1}{2}})}^{3}$ .

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Step 2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

7^{\frac{1}{2} \cdot 3}

$7^{\frac{1}{2} \cdot 3}$

Step 2.2

Combine

\frac{1}{2}

$\frac{1}{2}$ and

3

$3$ .

7^{\frac{3}{2}}

$7^{\frac{3}{2}}$

7^{\frac{3}{2}}

$7^{\frac{3}{2}}$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$