Basic Math Examples

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

Step 1

Rewrite $- 5$ as $- 1 (5)$ .

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

Step 2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

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

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

${(- 3 (i \cdot \sqrt{5}))}^{2}$

Step 4

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

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Step 4.1

Apply the product rule to $- 3 i \sqrt{5}$ .

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

Step 4.2

Apply the product rule to $- 3 i$ .

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

Step 5

Raise $- 3$ to the power of $2$ .

$9 i^{2} {\sqrt{5}}^{2}$

Step 6

Rewrite $i^{2}$ as $- 1$ .

$9 \cdot - 1 {\sqrt{5}}^{2}$

Step 7

Multiply $9$ by $- 1$ .

$- 9 {\sqrt{5}}^{2}$

Step 8

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

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Step 8.1

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

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

Step 8.2

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

$- 9 \cdot 5^{\frac{1}{2} \cdot 2}$

Step 8.3

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

$- 9 \cdot 5^{\frac{2}{2}}$

Step 8.4

Cancel the common factor of $2$ .

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Step 8.4.1

Cancel the common factor.

$- 9 \cdot 5^{\frac{2}{2}}$

Step 8.4.2

Rewrite the expression.

$- 9 \cdot 5^{1}$

Step 8.5

Evaluate the exponent.

$- 9 \cdot 5$

Step 9

Multiply $- 9$ by $5$ .

$- 45$