Basic Math Examples

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

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 $1$ .

$10^{4}$

Step 2

Raise $10$ to the power of $4$ .

$10000$