Evaluate ((3 square root of 3)/2)^2

${(\frac{3 \sqrt{3}}{2})}^{2}$

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

Apply the product rule to $\frac{3 \sqrt{3}}{2}$ .

$\frac{{(3 \sqrt{3})}^{2}}{2^{2}}$

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

$\frac{3^{2} {\sqrt{3}}^{2}}{2^{2}}$

Simplify the numerator.

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

$\frac{9 {\sqrt{3}}^{2}}{2^{2}}$

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

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

$\frac{9 {(3^{\frac{1}{2}})}^{2}}{2^{2}}$

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

$\frac{9 \cdot 3^{\frac{1}{2} \cdot 2}}{2^{2}}$

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

$\frac{9 \cdot 3^{\frac{2}{2}}}{2^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{9 \cdot 3^{\frac{2}{2}}}{2^{2}}$

Rewrite the expression.

$\frac{9 \cdot 3^{1}}{2^{2}}$

Evaluate the exponent.

$\frac{9 \cdot 3}{2^{2}}$

Simplify the expression.

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

$\frac{9 \cdot 3}{4}$

Multiply $9$ by $3$ .

$\frac{27}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{27}{4}$

Decimal Form:

$6.75$

Mixed Number Form:

$6 \frac{3}{4}$