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

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

Simplify each term.

Raise $4$ to the power of $3$ .

$\frac{3}{2} \cdot (64 - 2^{2} \cdot 3^{2})$

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

$\frac{3}{2} \cdot (64 - 1 \cdot 4 \cdot 3^{2})$

Multiply $- 1$ by $4$ .

$\frac{3}{2} \cdot (64 - 4 \cdot 3^{2})$

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

$\frac{3}{2} \cdot (64 - 4 \cdot 9)$

Multiply $- 4$ by $9$ .

$\frac{3}{2} \cdot (64 - 36)$

Reduce the expression by cancelling the common factors.

Subtract $36$ from $64$ .

$\frac{3}{2} \cdot 28$

Cancel the common factor of $2$ .

Factor $2$ out of $28$ .

$\frac{3}{2} \cdot (2 (14))$

Cancel the common factor.

$\frac{3}{2} \cdot (2 \cdot 14)$

Rewrite the expression.

$3 \cdot 14$

Multiply $3$ by $14$ .

$42$