Pre-Algebra Examples

$\frac{\frac{1}{\sqrt{(2) + 5}}}{5 (2) + 4}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{\sqrt{2 + 5}} \cdot \frac{1}{5 (2) + 4}$

Step 2

Add $2$ and $5$ .

$\frac{1}{\sqrt{7}} \cdot \frac{1}{5 (2) + 4}$

Step 3

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

$\frac{1}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}} \frac{1}{5 (2) + 4}$

Step 4

Combine and simplify the denominator.

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Step 4.1

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

$\frac{\sqrt{7}}{\sqrt{7} \sqrt{7}} \cdot \frac{1}{5 (2) + 4}$

Step 4.2

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

$\frac{\sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}} \cdot \frac{1}{5 (2) + 4}$

Step 4.3

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

$\frac{\sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}} \cdot \frac{1}{5 (2) + 4}$

Step 4.4

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

$\frac{\sqrt{7}}{{\sqrt{7}}^{1 + 1}} \cdot \frac{1}{5 (2) + 4}$

Step 4.5

Add $1$ and $1$ .

$\frac{\sqrt{7}}{{\sqrt{7}}^{2}} \cdot \frac{1}{5 (2) + 4}$

Step 4.6

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

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Step 4.6.1

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

$\frac{\sqrt{7}}{{(7^{\frac{1}{2}})}^{2}} \cdot \frac{1}{5 (2) + 4}$

Step 4.6.2

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

$\frac{\sqrt{7}}{7^{\frac{1}{2} \cdot 2}} \cdot \frac{1}{5 (2) + 4}$

Step 4.6.3

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

$\frac{\sqrt{7}}{7^{\frac{2}{2}}} \cdot \frac{1}{5 (2) + 4}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$\frac{\sqrt{7}}{7^{\frac{2}{2}}} \cdot \frac{1}{5 (2) + 4}$

Step 4.6.4.2

Rewrite the expression.

$\frac{\sqrt{7}}{7^{1}} \cdot \frac{1}{5 (2) + 4}$

Step 4.6.5

Evaluate the exponent.

$\frac{\sqrt{7}}{7} \cdot \frac{1}{5 (2) + 4}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $5$ by $2$ .

$\frac{\sqrt{7}}{7} \cdot \frac{1}{10 + 4}$

Step 5.2

Add $10$ and $4$ .

$\frac{\sqrt{7}}{7} \cdot \frac{1}{14}$

Step 6

Multiply $\frac{\sqrt{7}}{7} \cdot \frac{1}{14}$ .

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Step 6.1

Multiply $\frac{\sqrt{7}}{7}$ by $\frac{1}{14}$ .

$\frac{\sqrt{7}}{7 \cdot 14}$

Step 6.2

Multiply $7$ by $14$ .

$\frac{\sqrt{7}}{98}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{7}}{98}$

Decimal Form:

$0.02699746 \dots$