Simplify (3i square root of 5)^2

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

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

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

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

Apply the product rule to $3 i$ .

$3^{2} i^{2} {\sqrt{5}}^{2}$

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

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

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

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

Multiply $9$ by $- 1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$- 9 \cdot 5^{1}$

Evaluate the exponent.

$- 9 \cdot 5$

Multiply $- 9$ by $5$ .

$- 45$