Basic Math Examples

{(\sqrt{10})}^{8}

${(\sqrt{10})}^{8}$

Step 1

Rewrite

${\sqrt{10}}^{8}$ as

$10^{4}$ .

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Step 1.1

Use

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

$\sqrt{10}$ as

$10^{\frac{1}{2}}$ .

${(10^{\frac{1}{2}})}^{8}$

Step 1.2

Apply the power rule and multiply exponents,

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

$10^{\frac{1}{2} \cdot 8}$

Step 1.3

Combine

$\frac{1}{2}$ and

$8$ .

$10^{\frac{8}{2}}$

Step 1.4

Cancel the common factor of

$8$ and

$2$ .

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Step 1.4.1

Factor

$2$ out of

$8$ .

$10^{\frac{2 \cdot 4}{2}}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor

$2$ out of

$2$ .

$10^{\frac{2 \cdot 4}{2 (1)}}$

Step 1.4.2.2

Cancel the common factor.

$10^{\frac{2 \cdot 4}{2 \cdot 1}}$

Step 1.4.2.3

Rewrite the expression.

$10^{\frac{4}{1}}$

Step 1.4.2.4

Divide

$4$ by

$1$ .

$10^{4}$

$10^{4}$

$10^{4}$

$10^{4}$

Step 2

Raise

$10$ to the power of

$4$ .

$10000$

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