Simplify (-24m^5n^4)/(8m^-7n^-2)

$\frac{- 24 m^{5} n^{4}}{8 m^{- 7} n^{- 2}}$

Step 1

Move $m^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 24 m^{5} n^{4} m^{7}}{8 n^{- 2}}$

Step 2

Move $n^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 24 m^{5} n^{4} m^{7} n^{2}}{8}$

Step 3

Simplify the numerator.

Multiply $m^{5}$ by $m^{7}$ by adding the exponents.

Move $m^{7}$ .

$\frac{- 24 (m^{7} m^{5}) n^{4} n^{2}}{8}$

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

$\frac{- 24 m^{7 + 5} n^{4} n^{2}}{8}$

Add $7$ and $5$ .

$\frac{- 24 m^{12} n^{4} n^{2}}{8}$

Multiply $n^{4}$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$\frac{- 24 m^{12} (n^{2} n^{4})}{8}$

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

$\frac{- 24 m^{12} n^{2 + 4}}{8}$

Add $2$ and $4$ .

$\frac{- 24 m^{12} n^{6}}{8}$

Step 4

Cancel the common factor of $- 24$ and $8$ .

Factor $8$ out of $- 24 m^{12} n^{6}$ .

$\frac{8 (- 3 m^{12} n^{6})}{8}$

Cancel the common factors.

Factor $8$ out of $8$ .

$\frac{8 (- 3 m^{12} n^{6})}{8 (1)}$

Cancel the common factor.

$\frac{8 (- 3 m^{12} n^{6})}{8 \cdot 1}$

Rewrite the expression.

$\frac{- 3 m^{12} n^{6}}{1}$

Divide $- 3 m^{12} n^{6}$ by $1$ .

$- 3 m^{12} n^{6}$