Algebra Examples

$- \frac{4}{\sqrt{1 - 16 {(- \frac{1}{6})}^{2}}}$

Step 1

Simplify the denominator.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{1}{6}$ .

$- \frac{4}{\sqrt{1 - 16 ({(- 1)}^{2} {(\frac{1}{6})}^{2})}}$

Step 1.1.2

Apply the product rule to $\frac{1}{6}$ .

$- \frac{4}{\sqrt{1 - 16 ({(- 1)}^{2} \frac{1^{2}}{6^{2}})}}$

Step 1.2

Raise $- 1$ to the power of $2$ .

$- \frac{4}{\sqrt{1 - 16 (1 \frac{1^{2}}{6^{2}})}}$

Step 1.3

Multiply $\frac{1^{2}}{6^{2}}$ by $1$ .

$- \frac{4}{\sqrt{1 - 16 \frac{1^{2}}{6^{2}}}}$

Step 1.4

One to any power is one.

$- \frac{4}{\sqrt{1 - 16 \frac{1}{6^{2}}}}$

Step 1.5

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

$- \frac{4}{\sqrt{1 - 16 (\frac{1}{36})}}$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Factor $4$ out of $- 16$ .

$- \frac{4}{\sqrt{1 + 4 (- 4) \frac{1}{36}}}$

Step 1.6.2

Factor $4$ out of $36$ .

$- \frac{4}{\sqrt{1 + 4 \cdot - 4 \frac{1}{4 \cdot 9}}}$

Step 1.6.3

Cancel the common factor.

$- \frac{4}{\sqrt{1 + 4 \cdot - 4 \frac{1}{4 \cdot 9}}}$

Step 1.6.4

Rewrite the expression.

$- \frac{4}{\sqrt{1 - 4 (\frac{1}{9})}}$

Step 1.7

Combine $- 4$ and $\frac{1}{9}$ .

$- \frac{4}{\sqrt{1 + \frac{- 4}{9}}}$

Step 1.8

Move the negative in front of the fraction.

$- \frac{4}{\sqrt{1 - \frac{4}{9}}}$

Step 1.9

Write $1$ as a fraction with a common denominator.

$- \frac{4}{\sqrt{\frac{9}{9} - \frac{4}{9}}}$

Step 1.10

Combine the numerators over the common denominator.

$- \frac{4}{\sqrt{\frac{9 - 4}{9}}}$

Step 1.11

Subtract $4$ from $9$ .

$- \frac{4}{\sqrt{\frac{5}{9}}}$

Step 1.12

Rewrite $\sqrt{\frac{5}{9}}$ as $\frac{\sqrt{5}}{\sqrt{9}}$ .

$- \frac{4}{\frac{\sqrt{5}}{\sqrt{9}}}$

Step 1.13

Simplify the denominator.

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Step 1.13.1

Rewrite $9$ as $3^{2}$ .

$- \frac{4}{\frac{\sqrt{5}}{\sqrt{3^{2}}}}$

Step 1.13.2

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{4}{\frac{\sqrt{5}}{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$- (4 \frac{3}{\sqrt{5}})$

Step 3

Multiply $\frac{3}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$- (4 (\frac{3}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}}))$

Step 4

Combine and simplify the denominator.

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Step 4.1

Multiply $\frac{3}{\sqrt{5}}$ by $\frac{\sqrt{5}}{\sqrt{5}}$ .

$- (4 \frac{3 \sqrt{5}}{\sqrt{5} \sqrt{5}})$

Step 4.2

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

$- (4 \frac{3 \sqrt{5}}{{\sqrt{5}}^{1} \sqrt{5}})$

Step 4.3

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

$- (4 \frac{3 \sqrt{5}}{{\sqrt{5}}^{1} {\sqrt{5}}^{1}})$

Step 4.4

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

$- (4 \frac{3 \sqrt{5}}{{\sqrt{5}}^{1 + 1}})$

Step 4.5

Add $1$ and $1$ .

$- (4 \frac{3 \sqrt{5}}{{\sqrt{5}}^{2}})$

Step 4.6

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Step 4.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$- (4 \frac{3 \sqrt{5}}{{(5^{\frac{1}{2}})}^{2}})$

Step 4.6.2

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

$- (4 \frac{3 \sqrt{5}}{5^{\frac{1}{2} \cdot 2}})$

Step 4.6.3

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

$- (4 \frac{3 \sqrt{5}}{5^{\frac{2}{2}}})$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$- (4 \frac{3 \sqrt{5}}{5^{\frac{2}{2}}})$

Step 4.6.4.2

Rewrite the expression.

$- (4 \frac{3 \sqrt{5}}{5^{1}})$

Step 4.6.5

Evaluate the exponent.

$- (4 \frac{3 \sqrt{5}}{5})$

Step 5

Multiply $4 \frac{3 \sqrt{5}}{5}$ .

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Step 5.1

Combine $4$ and $\frac{3 \sqrt{5}}{5}$ .

$- \frac{4 (3 \sqrt{5})}{5}$

Step 5.2

Multiply $3$ by $4$ .

$- \frac{12 \sqrt{5}}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{12 \sqrt{5}}{5}$

Decimal Form:

$- 5.36656314 \dots$