Evaluate -3/( square root of 1-9(-1/5)^2)

$- \frac{3}{\sqrt{1 - 9 {(- \frac{1}{5})}^{2}}}$

Step 1

Simplify the denominator.

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

Apply the product rule to $- \frac{1}{5}$ .

$- \frac{3}{\sqrt{1 - 9 ({(- 1)}^{2} {(\frac{1}{5})}^{2})}}$

Apply the product rule to $\frac{1}{5}$ .

$- \frac{3}{\sqrt{1 - 9 ({(- 1)}^{2} \frac{1^{2}}{5^{2}})}}$

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

$- \frac{3}{\sqrt{1 - 9 (1 \frac{1^{2}}{5^{2}})}}$

Multiply $\frac{1^{2}}{5^{2}}$ by $1$ .

$- \frac{3}{\sqrt{1 - 9 \frac{1^{2}}{5^{2}}}}$

One to any power is one.

$- \frac{3}{\sqrt{1 - 9 \frac{1}{5^{2}}}}$

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

$- \frac{3}{\sqrt{1 - 9 (\frac{1}{25})}}$

Combine $- 9$ and $\frac{1}{25}$ .

$- \frac{3}{\sqrt{1 + \frac{- 9}{25}}}$

Move the negative in front of the fraction.

$- \frac{3}{\sqrt{1 - \frac{9}{25}}}$

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

$- \frac{3}{\sqrt{\frac{25}{25} - \frac{9}{25}}}$

Combine the numerators over the common denominator.

$- \frac{3}{\sqrt{\frac{25 - 9}{25}}}$

Subtract $9$ from $25$ .

$- \frac{3}{\sqrt{\frac{16}{25}}}$

Rewrite $\sqrt{\frac{16}{25}}$ as $\frac{\sqrt{16}}{\sqrt{25}}$ .

$- \frac{3}{\frac{\sqrt{16}}{\sqrt{25}}}$

Simplify the numerator.

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

$- \frac{3}{\frac{\sqrt{4^{2}}}{\sqrt{25}}}$

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

$- \frac{3}{\frac{4}{\sqrt{25}}}$

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

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

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

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

Multiply $3 (\frac{5}{4})$ .

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

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

Multiply $3$ by $5$ .

$- \frac{15}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{15}{4}$

Decimal Form:

$- 3.75$

Mixed Number Form:

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

Evaluate -3/( square root of 1-9(-1/5)^2)

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