Evaluate 4(-3/2)^2-3

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

Simplify each term.

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

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

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

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

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

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

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

Multiply $\frac{3^{2}}{2^{2}}$ by $1$ .

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

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

$4 \frac{9}{2^{2}} - 3$

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

$4 (\frac{9}{4}) - 3$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 (\frac{9}{4}) - 3$

Rewrite the expression.

$9 - 3$

Subtract $3$ from $9$ .

$6$