Simplify (-3m^3n)^2(2m^2n^4)

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Apply the product rule to $- 3 m^{3} n$ .

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

Apply the product rule to $- 3 m^{3}$ .

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

Step 3

Multiply $n^{2}$ by $n^{4}$ by adding the exponents.

Move $n^{4}$ .

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

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

$2 ({(- 3)}^{2} {(m^{3})}^{2} n^{4 + 2}) m^{2}$

Add $4$ and $2$ .

$2 ({(- 3)}^{2} {(m^{3})}^{2} n^{6}) m^{2}$

Step 4

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

$2 (9 {(m^{3})}^{2} n^{6}) m^{2}$

Step 5

Multiply the exponents in ${(m^{3})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 (9 m^{3 \cdot 2} n^{6}) m^{2}$

Multiply $3$ by $2$ .

$2 (9 m^{6} n^{6}) m^{2}$

Step 6

Multiply $m^{6}$ by $m^{2}$ by adding the exponents.

Move $m^{2}$ .

$2 (9 (m^{2} m^{6}) n^{6})$

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

$2 (9 m^{2 + 6} n^{6})$

Add $2$ and $6$ .

$2 (9 m^{8} n^{6})$

Step 7

Multiply $9$ by $2$ .

$18 m^{8} n^{6}$