Evaluate (-9/2)^2

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

Step 1

Move the negative in front of the fraction.

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

Step 2

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

Apply the product rule to $- \frac{9}{2}$ .

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

Apply the product rule to $\frac{9}{2}$ .

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

Step 3

Raise $- 1$ to the power of $2$ .

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

Step 4

Multiply $\frac{9^{2}}{2^{2}}$ by $1$ .

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

Step 5

Raise $9$ to the power of $2$ .

$\frac{81}{2^{2}}$

Step 6

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

$\frac{81}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{4}$

Decimal Form:

$20.25$

Mixed Number Form:

$20 \frac{1}{4}$