Evaluate ((3pi)/2)^2

${(\frac{3 π}{2})}^{2}$

Step 1

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

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

$\frac{{(3 π)}^{2}}{2^{2}}$

Apply the product rule to $3 π$ .

$\frac{3^{2} π^{2}}{2^{2}}$

Step 2

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

$\frac{9 π^{2}}{2^{2}}$

Step 3

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

$\frac{9 π^{2}}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{9 π^{2}}{4}$

Decimal Form:

$22.20660990 \dots$