Algebra Examples

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

Step 1

Simplify the denominator.

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Step 1.1

Apply the product rule to $\frac{1}{4}$ .

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

Step 1.2

One to any power is one.

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

Step 1.3

Raise $4$ to the power of $2$ .

$- \frac{1}{\sqrt{1 - \frac{1}{16}}}$

Step 1.4

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

$- \frac{1}{\sqrt{\frac{16}{16} - \frac{1}{16}}}$

Step 1.5

Combine the numerators over the common denominator.

$- \frac{1}{\sqrt{\frac{16 - 1}{16}}}$

Step 1.6

Subtract $1$ from $16$ .

$- \frac{1}{\sqrt{\frac{15}{16}}}$

Step 1.7

Rewrite $\sqrt{\frac{15}{16}}$ as $\frac{\sqrt{15}}{\sqrt{16}}$ .

$- \frac{1}{\frac{\sqrt{15}}{\sqrt{16}}}$

Step 1.8

Simplify the denominator.

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Step 1.8.1

Rewrite $16$ as $4^{2}$ .

$- \frac{1}{\frac{\sqrt{15}}{\sqrt{4^{2}}}}$

Step 1.8.2

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

$- \frac{1}{\frac{\sqrt{15}}{4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$- (1 \frac{4}{\sqrt{15}})$

Step 3

Multiply $\frac{4}{\sqrt{15}}$ by $1$ .

$- \frac{4}{\sqrt{15}}$

Step 4

Multiply $\frac{4}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$- (\frac{4}{\sqrt{15}} \cdot \frac{\sqrt{15}}{\sqrt{15}})$

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{4}{\sqrt{15}}$ by $\frac{\sqrt{15}}{\sqrt{15}}$ .

$- \frac{4 \sqrt{15}}{\sqrt{15} \sqrt{15}}$

Step 5.2

Raise $\sqrt{15}$ to the power of $1$ .

$- \frac{4 \sqrt{15}}{{\sqrt{15}}^{1} \sqrt{15}}$

Step 5.3

Raise $\sqrt{15}$ to the power of $1$ .

$- \frac{4 \sqrt{15}}{{\sqrt{15}}^{1} {\sqrt{15}}^{1}}$

Step 5.4

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

$- \frac{4 \sqrt{15}}{{\sqrt{15}}^{1 + 1}}$

Step 5.5

Add $1$ and $1$ .

$- \frac{4 \sqrt{15}}{{\sqrt{15}}^{2}}$

Step 5.6

Rewrite ${\sqrt{15}}^{2}$ as $15$ .

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Step 5.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{15}$ as $15^{\frac{1}{2}}$ .

$- \frac{4 \sqrt{15}}{{(15^{\frac{1}{2}})}^{2}}$

Step 5.6.2

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

$- \frac{4 \sqrt{15}}{15^{\frac{1}{2} \cdot 2}}$

Step 5.6.3

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

$- \frac{4 \sqrt{15}}{15^{\frac{2}{2}}}$

Step 5.6.4

Cancel the common factor of $2$ .

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Step 5.6.4.1

Cancel the common factor.

$- \frac{4 \sqrt{15}}{15^{\frac{2}{2}}}$

Step 5.6.4.2

Rewrite the expression.

$- \frac{4 \sqrt{15}}{15^{1}}$

Step 5.6.5

Evaluate the exponent.

$- \frac{4 \sqrt{15}}{15}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{4 \sqrt{15}}{15}$

Decimal Form:

$- 1.03279555 \dots$