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

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

Step 1

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

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

Step 2

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

Move $n^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Step 3

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

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

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

Multiply $3$ by $2$ .

$2 m^{4} n^{4} m^{6}$

Step 4

Multiply $m^{4}$ by $m^{6}$ by adding the exponents.

Move $m^{6}$ .

$2 (m^{6} m^{4}) n^{4}$

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

$2 m^{6 + 4} n^{4}$

Add $6$ and $4$ .

$2 m^{10} n^{4}$