Simplify (3m)(4m)^2

$(3 m) {(4 m)}^{2}$

Step 1

Apply the product rule to $4 m$ .

$3 m (4^{2} m^{2})$

Step 2

Rewrite using the commutative property of multiplication.

$3 \cdot 4^{2} m \cdot m^{2}$

Step 3

Multiply $m$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$3 \cdot 4^{2} (m^{2} m)$

Multiply $m^{2}$ by $m$ .

Raise $m$ to the power of $1$ .

$3 \cdot 4^{2} (m^{2} m^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \cdot 4^{2} m^{2 + 1}$

Add $2$ and $1$ .

$3 \cdot 4^{2} m^{3}$

Step 4

Raise $4$ to the power of $2$ .

$3 \cdot 16 m^{3}$

Step 5

Multiply $3$ by $16$ .

$48 m^{3}$