Divide (m^-6n^-3)/(m^-13n^-1)

$\frac{m^{- 6} n^{- 3}}{m^{- 13} n^{- 1}}$

Step 1

Move $n^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{m^{- 6}}{m^{- 13} n^{- 1} n^{3}}$

Step 2

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

Move $n^{3}$ .

$\frac{m^{- 6}}{m^{- 13} (n^{3} n^{- 1})}$

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

$\frac{m^{- 6}}{m^{- 13} n^{3 - 1}}$

Subtract $1$ from $3$ .

$\frac{m^{- 6}}{m^{- 13} n^{2}}$

Step 3

Move $m^{- 13}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{m^{- 6} m^{13}}{n^{2}}$

Step 4

Multiply $m^{- 6}$ by $m^{13}$ by adding the exponents.

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

$\frac{m^{- 6 + 13}}{n^{2}}$

Add $- 6$ and $13$ .

$\frac{m^{7}}{n^{2}}$