Basic Math Examples

$\frac{\sqrt{\frac{1}{7}} \cdot 1}{7} \cdot \sqrt{7}$

Step 1

Multiply $\sqrt{\frac{1}{7}}$ by $1$ .

$\frac{\sqrt{\frac{1}{7}}}{7} \cdot \sqrt{7}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $\sqrt{\frac{1}{7}}$ as $\frac{\sqrt{1}}{\sqrt{7}}$ .

$\frac{\frac{\sqrt{1}}{\sqrt{7}}}{7} \cdot \sqrt{7}$

Step 2.2

Any root of $1$ is $1$ .

$\frac{\frac{1}{\sqrt{7}}}{7} \cdot \sqrt{7}$

Step 2.3

Multiply $\frac{1}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\frac{1}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}}{7} \cdot \sqrt{7}$

Step 2.4

Combine and simplify the denominator.

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Step 2.4.1

Multiply $\frac{1}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{\frac{\sqrt{7}}{\sqrt{7} \sqrt{7}}}{7} \cdot \sqrt{7}$

Step 2.4.2

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\frac{\sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}}{7} \cdot \sqrt{7}$

Step 2.4.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\frac{\sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}}{7} \cdot \sqrt{7}$

Step 2.4.4

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

$\frac{\frac{\sqrt{7}}{{\sqrt{7}}^{1 + 1}}}{7} \cdot \sqrt{7}$

Step 2.4.5

Add $1$ and $1$ .

$\frac{\frac{\sqrt{7}}{{\sqrt{7}}^{2}}}{7} \cdot \sqrt{7}$

Step 2.4.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 2.4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{\frac{\sqrt{7}}{{(7^{\frac{1}{2}})}^{2}}}{7} \cdot \sqrt{7}$

Step 2.4.6.2

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

$\frac{\frac{\sqrt{7}}{7^{\frac{1}{2} \cdot 2}}}{7} \cdot \sqrt{7}$

Step 2.4.6.3

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

$\frac{\frac{\sqrt{7}}{7^{\frac{2}{2}}}}{7} \cdot \sqrt{7}$

Step 2.4.6.4

Cancel the common factor of $2$ .

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Step 2.4.6.4.1

Cancel the common factor.

$\frac{\frac{\sqrt{7}}{7^{\frac{2}{2}}}}{7} \cdot \sqrt{7}$

Step 2.4.6.4.2

Rewrite the expression.

$\frac{\frac{\sqrt{7}}{7^{1}}}{7} \cdot \sqrt{7}$

Step 2.4.6.5

Evaluate the exponent.

$\frac{\frac{\sqrt{7}}{7}}{7} \cdot \sqrt{7}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{\sqrt{7}}{7} \cdot \frac{1}{7} \cdot \sqrt{7}$

Step 4

Multiply $\frac{\sqrt{7}}{7} \cdot \frac{1}{7}$ .

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Step 4.1

Multiply $\frac{\sqrt{7}}{7}$ by $\frac{1}{7}$ .

$\frac{\sqrt{7}}{7 \cdot 7} \cdot \sqrt{7}$

Step 4.2

Multiply $7$ by $7$ .

$\frac{\sqrt{7}}{49} \cdot \sqrt{7}$

Step 5

Multiply $\frac{\sqrt{7}}{49} \sqrt{7}$ .

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Step 5.1

Combine $\frac{\sqrt{7}}{49}$ and $\sqrt{7}$ .

$\frac{\sqrt{7} \sqrt{7}}{49}$

Step 5.2

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{{\sqrt{7}}^{1} \sqrt{7}}{49}$

Step 5.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}{49}$

Step 5.4

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

$\frac{{\sqrt{7}}^{1 + 1}}{49}$

Step 5.5

Add $1$ and $1$ .

$\frac{{\sqrt{7}}^{2}}{49}$

Step 6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\frac{{(7^{\frac{1}{2}})}^{2}}{49}$

Step 6.2

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

$\frac{7^{\frac{1}{2} \cdot 2}}{49}$

Step 6.3

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

$\frac{7^{\frac{2}{2}}}{49}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$\frac{7^{\frac{2}{2}}}{49}$

Step 6.4.2

Rewrite the expression.

$\frac{7^{1}}{49}$

Step 6.5

Evaluate the exponent.

$\frac{7}{49}$

Step 7

Cancel the common factor of $7$ and $49$ .

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Step 7.1

Factor $7$ out of $7$ .

$\frac{7 (1)}{49}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $7$ out of $49$ .

$\frac{7 \cdot 1}{7 \cdot 7}$

Step 7.2.2

Cancel the common factor.

$\frac{7 \cdot 1}{7 \cdot 7}$

Step 7.2.3

Rewrite the expression.

$\frac{1}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{7}$

Decimal Form:

$0.\overline{142857}$