Evaluate (5m^-1n^2)(-3m^3n)

$(5 m^{- 1} n^{2}) (- 3 m^{3} n)$

Step 1

Multiply $m^{- 1}$ by $m^{3}$ by adding the exponents.

Move $m^{3}$ .

$5 (m^{3} m^{- 1}) n^{2} (- 3 n)$

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

$5 m^{3 - 1} n^{2} (- 3 n)$

Subtract $1$ from $3$ .

$5 m^{2} n^{2} (- 3 n)$

Step 2

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

Move $n$ .

$5 m^{2} (n \cdot n^{2}) \cdot - 3$

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

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

$5 m^{2} (n^{1} n^{2}) \cdot - 3$

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

$5 m^{2} n^{1 + 2} \cdot - 3$

Add $1$ and $2$ .

$5 m^{2} n^{3} \cdot - 3$

Step 3

Multiply $- 3$ by $5$ .

$- 15 m^{2} n^{3}$