Precalculus Examples

${(\sqrt[5]{6})}^{- 10}$

Step 1

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

$\frac{1}{{\sqrt[5]{6}}^{10}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite ${\sqrt[5]{6}}^{10}$ as $6^{2}$ .

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Step 2.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{6}$ as $6^{\frac{1}{5}}$ .

$\frac{1}{{(6^{\frac{1}{5}})}^{10}}$

Step 2.1.2

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

$\frac{1}{6^{\frac{1}{5} \cdot 10}}$

Step 2.1.3

Combine $\frac{1}{5}$ and $10$ .

$\frac{1}{6^{\frac{10}{5}}}$

Step 2.1.4

Cancel the common factor of $10$ and $5$ .

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Step 2.1.4.1

Factor $5$ out of $10$ .

$\frac{1}{6^{\frac{5 \cdot 2}{5}}}$

Step 2.1.4.2

Cancel the common factors.

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Step 2.1.4.2.1

Factor $5$ out of $5$ .

$\frac{1}{6^{\frac{5 \cdot 2}{5 (1)}}}$

Step 2.1.4.2.2

Cancel the common factor.

$\frac{1}{6^{\frac{5 \cdot 2}{5 \cdot 1}}}$

Step 2.1.4.2.3

Rewrite the expression.

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

Step 2.1.4.2.4

Divide $2$ by $1$ .

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

Step 2.2

Raise $6$ to the power of $2$ .

$\frac{1}{36}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{36}$

Decimal Form:

$0.02\overline{7}$