Simplify (2m^-3)(-mn)^3

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Combine $2$ and $\frac{1}{m^{3}}$ .

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

Step 3

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

Apply the product rule to $- m n$ .

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

Apply the product rule to $- m$ .

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

Step 4

Simplify the expression.

Rewrite using the commutative property of multiplication.

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

Raise $- 1$ to the power of $3$ .

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

Step 5

Cancel the common factor of $m^{3}$ .

Move the leading negative in $- \frac{2}{m^{3}}$ into the numerator.

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

Factor $m^{3}$ out of $m^{3} n^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- 2 n^{3}$