Basic Math Examples

${(\sqrt[12]{\frac{1}{5}})}^{24}$

Step 1

Rewrite $\sqrt[12]{\frac{1}{5}}$ as $\frac{\sqrt[12]{1}}{\sqrt[12]{5}}$ .

${(\frac{\sqrt[12]{1}}{\sqrt[12]{5}})}^{24}$

Step 2

Any root of $1$ is $1$ .

${(\frac{1}{\sqrt[12]{5}})}^{24}$

Step 3

Simplify the expression.

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Step 3.1

Apply the product rule to $\frac{1}{\sqrt[12]{5}}$ .

$\frac{1^{24}}{{\sqrt[12]{5}}^{24}}$

Step 3.2

One to any power is one.

$\frac{1}{{\sqrt[12]{5}}^{24}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite ${\sqrt[12]{5}}^{24}$ as $5^{2}$ .

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Step 4.1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[12]{5}$ as $5^{\frac{1}{12}}$ .

$\frac{1}{{(5^{\frac{1}{12}})}^{24}}$

Step 4.1.2

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

$\frac{1}{5^{\frac{1}{12} \cdot 24}}$

Step 4.1.3

Combine $\frac{1}{12}$ and $24$ .

$\frac{1}{5^{\frac{24}{12}}}$

Step 4.1.4

Cancel the common factor of $24$ and $12$ .

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Step 4.1.4.1

Factor $12$ out of $24$ .

$\frac{1}{5^{\frac{12 \cdot 2}{12}}}$

Step 4.1.4.2

Cancel the common factors.

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Step 4.1.4.2.1

Factor $12$ out of $12$ .

$\frac{1}{5^{\frac{12 \cdot 2}{12 (1)}}}$

Step 4.1.4.2.2

Cancel the common factor.

$\frac{1}{5^{\frac{12 \cdot 2}{12 \cdot 1}}}$

Step 4.1.4.2.3

Rewrite the expression.

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

Step 4.1.4.2.4

Divide $2$ by $1$ .

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

Step 4.2

Raise $5$ to the power of $2$ .

$\frac{1}{25}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$