Simplify -(-i square root of -3)^4

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

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

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

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

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

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

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

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

Tap for more steps…

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Multiply.

Tap for more steps…

Multiply $- 1$ by $- 1$ .

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

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

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

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

Tap for more steps…

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

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

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

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

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

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

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

Tap for more steps…

Factor $2$ out of $4$ .

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

Cancel the common factors.

Tap for more steps…

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2$ by $1$ .

$- 3^{2}$

Simplify the expression.

Tap for more steps…

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

$- 1 \cdot 9$

Multiply $- 1$ by $9$ .

$- 9$

Simplify -(-i square root of -3)^4

Solving MATH problems