Simplify ((-4m)^3)/(10m^-5)

$\frac{{(- 4 m)}^{3}}{10 m^{- 5}}$

Step 1

Move $m^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(- 4 m)}^{3} m^{5}}{10}$

Step 2

Simplify the numerator.

Apply the product rule to $- 4 m$ .

$\frac{{(- 4)}^{3} m^{3} m^{5}}{10}$

Multiply $m^{3}$ by $m^{5}$ by adding the exponents.

Move $m^{5}$ .

$\frac{{(- 4)}^{3} (m^{5} m^{3})}{10}$

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

$\frac{{(- 4)}^{3} m^{5 + 3}}{10}$

Add $5$ and $3$ .

$\frac{{(- 4)}^{3} m^{8}}{10}$

Raise $- 4$ to the power of $3$ .

$\frac{- 64 m^{8}}{10}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 64$ and $10$ .

Factor $2$ out of $- 64 m^{8}$ .

$\frac{2 (- 32 m^{8})}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 (- 32 m^{8})}{2 (5)}$

Cancel the common factor.

$\frac{2 (- 32 m^{8})}{2 \cdot 5}$

Rewrite the expression.

$\frac{- 32 m^{8}}{5}$

Move the negative in front of the fraction.

$- \frac{32 m^{8}}{5}$