Basic Math Examples

${(\sqrt[10]{\frac{1}{10}})}^{2}$

Step 1

Rewrite $\sqrt[10]{\frac{1}{10}}$ as $\frac{\sqrt[10]{1}}{\sqrt[10]{10}}$ .

${(\frac{\sqrt[10]{1}}{\sqrt[10]{10}})}^{2}$

Step 2

Any root of $1$ is $1$ .

${(\frac{1}{\sqrt[10]{10}})}^{2}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{1}{\sqrt[10]{10}}$ .

$\frac{1^{2}}{{\sqrt[10]{10}}^{2}}$

Step 3.2

One to any power is one.

$\frac{1}{{\sqrt[10]{10}}^{2}}$

Step 4

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

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[10]{10}$ as $10^{\frac{1}{10}}$ .

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

Step 4.2

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

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

Step 4.3

Combine $\frac{1}{10}$ and $2$ .

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

Step 4.4

Cancel the common factor of $2$ and $10$ .

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Step 4.4.1

Factor $2$ out of $2$ .

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

Step 4.4.2

Cancel the common factors.

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Step 4.4.2.1

Factor $2$ out of $10$ .

$\frac{1}{10^{\frac{2 \cdot 1}{2 \cdot 5}}}$

Step 4.4.2.2

Cancel the common factor.

$\frac{1}{10^{\frac{2 \cdot 1}{2 \cdot 5}}}$

Step 4.4.2.3

Rewrite the expression.

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

Step 4.5

Rewrite $10^{\frac{1}{5}}$ as $\sqrt[5]{10}$ .

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

Step 5

Multiply $\frac{1}{\sqrt[5]{10}}$ by $\frac{{\sqrt[5]{10}}^{4}}{{\sqrt[5]{10}}^{4}}$ .

$\frac{1}{\sqrt[5]{10}} \cdot \frac{{\sqrt[5]{10}}^{4}}{{\sqrt[5]{10}}^{4}}$

Step 6

Combine and simplify the denominator.

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Step 6.1

Multiply $\frac{1}{\sqrt[5]{10}}$ by $\frac{{\sqrt[5]{10}}^{4}}{{\sqrt[5]{10}}^{4}}$ .

$\frac{{\sqrt[5]{10}}^{4}}{\sqrt[5]{10} {\sqrt[5]{10}}^{4}}$

Step 6.2

Raise $\sqrt[5]{10}$ to the power of $1$ .

$\frac{{\sqrt[5]{10}}^{4}}{{\sqrt[5]{10}}^{1} {\sqrt[5]{10}}^{4}}$

Step 6.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sqrt[5]{10}}^{4}}{{\sqrt[5]{10}}^{1 + 4}}$

Step 6.4

Add $1$ and $4$ .

$\frac{{\sqrt[5]{10}}^{4}}{{\sqrt[5]{10}}^{5}}$

Step 6.5

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

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Step 6.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{10}$ as $10^{\frac{1}{5}}$ .

$\frac{{\sqrt[5]{10}}^{4}}{{(10^{\frac{1}{5}})}^{5}}$

Step 6.5.2

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

$\frac{{\sqrt[5]{10}}^{4}}{10^{\frac{1}{5} \cdot 5}}$

Step 6.5.3

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

$\frac{{\sqrt[5]{10}}^{4}}{10^{\frac{5}{5}}}$

Step 6.5.4

Cancel the common factor of $5$ .

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Step 6.5.4.1

Cancel the common factor.

$\frac{{\sqrt[5]{10}}^{4}}{10^{\frac{5}{5}}}$

Step 6.5.4.2

Rewrite the expression.

$\frac{{\sqrt[5]{10}}^{4}}{10^{1}}$

Step 6.5.5

Evaluate the exponent.

$\frac{{\sqrt[5]{10}}^{4}}{10}$

Step 7

Simplify the numerator.

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Step 7.1

Rewrite ${\sqrt[5]{10}}^{4}$ as $\sqrt[5]{10^{4}}$ .

$\frac{\sqrt[5]{10^{4}}}{10}$

Step 7.2

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

$\frac{\sqrt[5]{10000}}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt[5]{10000}}{10}$

Decimal Form:

$0.63095734 \dots$