Simplify (6m)(7m^2n)(n^4)

$(6 m) (7 m^{2} n) (n^{4})$

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

Move $m^{2}$ .

$6 (m^{2} m) (7 n) n^{4}$

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

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

$6 (m^{2} m^{1}) (7 n) n^{4}$

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

$6 m^{2 + 1} (7 n) n^{4}$

Add $2$ and $1$ .

$6 m^{3} (7 n) n^{4}$

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

Move $n^{4}$ .

$6 m^{3} (7 (n^{4} n))$

Multiply $n^{4}$ by $n$ .

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

$6 m^{3} (7 (n^{4} n^{1}))$

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

$6 m^{3} (7 n^{4 + 1})$

Add $4$ and $1$ .

$6 m^{3} (7 n^{5})$

Rewrite using the commutative property of multiplication.

$6 \cdot 7 m^{3} n^{5}$

Multiply $6$ by $7$ .

$42 m^{3} n^{5}$