Basic Math Examples

${(\sqrt[4]{36})}^{- 2}$

Step 1

Rewrite $36$ as $6^{2}$ .

${\sqrt[4]{6^{2}}}^{- 2}$

Step 2

Rewrite $\sqrt[4]{6^{2}}$ as $\sqrt{\sqrt{6^{2}}}$ .

${\sqrt{\sqrt{6^{2}}}}^{- 2}$

Step 3

Pull terms out from under the radical, assuming positive real numbers.

${\sqrt{6}}^{- 2}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{\sqrt{6}}^{2}}$

Step 5

Rewrite ${\sqrt{6}}^{2}$ as $6$ .

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Step 5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6}$ as $6^{\frac{1}{2}}$ .

$\frac{1}{{(6^{\frac{1}{2}})}^{2}}$

Step 5.2

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

$\frac{1}{6^{\frac{1}{2} \cdot 2}}$

Step 5.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{1}{6^{\frac{2}{2}}}$

Step 5.4

Cancel the common factor of $2$ .

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Step 5.4.1

Cancel the common factor.

$\frac{1}{6^{\frac{2}{2}}}$

Step 5.4.2

Rewrite the expression.

$\frac{1}{6^{1}}$

Step 5.5

Evaluate the exponent.

$\frac{1}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{6}$

Decimal Form:

$0.1\overline{6}$