Basic Math Examples

$- {(- i \sqrt{- 3})}^{4}$

Step 1

Rewrite $- 3$ as $- 1 (3)$ .

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

Step 2

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$- {(- i (\sqrt{- 1} \cdot \sqrt{3}))}^{4}$

Step 3

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

$- {(- i (i \cdot \sqrt{3}))}^{4}$

Step 4

Multiply $- i (i \sqrt{3})$ .

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

Multiply.

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Step 6.1

Multiply $- 1$ by $- 1$ .

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

Step 6.2

Multiply $\sqrt{3}$ by $1$ .

$- {\sqrt{3}}^{4}$

Step 7

Rewrite ${\sqrt{3}}^{4}$ as $3^{2}$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 7.2

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

$- 3^{\frac{1}{2} \cdot 4}$

Step 7.3

Combine $\frac{1}{2}$ and $4$ .

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

Step 7.4

Cancel the common factor of $4$ and $2$ .

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Step 7.4.1

Factor $2$ out of $4$ .

$- 3^{\frac{2 \cdot 2}{2}}$

Step 7.4.2

Cancel the common factors.

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Step 7.4.2.1

Factor $2$ out of $2$ .

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

Step 7.4.2.2

Cancel the common factor.

$- 3^{\frac{2 \cdot 2}{2 \cdot 1}}$

Step 7.4.2.3

Rewrite the expression.

$- 3^{\frac{2}{1}}$

Step 7.4.2.4

Divide $2$ by $1$ .

$- 3^{2}$

Step 8

Simplify the expression.

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Step 8.1

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

$- 1 \cdot 9$

Step 8.2

Multiply $- 1$ by $9$ .

$- 9$