Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Multiply $i (i \sqrt{5})$ .

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Step 4.1

Raise $i$ to the power of $1$ .

${(i^{1} i \sqrt{5})}^{2}$

Step 4.2

Raise $i$ to the power of $1$ .

${(i^{1} i^{1} \sqrt{5})}^{2}$

Step 4.3

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

${(i^{1 + 1} \sqrt{5})}^{2}$

Step 4.4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

Simplify the expression.

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Step 6.1

Rewrite $- 1 \sqrt{5}$ as $- \sqrt{5}$ .

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

Step 6.2

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

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

Step 6.3

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

$1 {\sqrt{5}}^{2}$

Step 6.4

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

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

Step 7

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

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Step 7.1

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

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

Step 7.2

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

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

Step 7.3

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

$5^{\frac{2}{2}}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$5^{\frac{2}{2}}$

Step 7.4.2

Rewrite the expression.

$5^{1}$

Step 7.5

Evaluate the exponent.

$5$