Simplify (m^2n^5)/(n^7m^-6)

$\frac{m^{2} n^{5}}{n^{7} m^{- 6}}$

Step 1

Move $m^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{m^{2} n^{5} m^{6}}{n^{7}}$

Step 2

Multiply $m^{2}$ by $m^{6}$ by adding the exponents.

Move $m^{6}$ .

$\frac{m^{6} m^{2} n^{5}}{n^{7}}$

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

$\frac{m^{6 + 2} n^{5}}{n^{7}}$

Add $6$ and $2$ .

$\frac{m^{8} n^{5}}{n^{7}}$

Step 3

Cancel the common factor of $n^{5}$ and $n^{7}$ .

Factor $n^{5}$ out of $m^{8} n^{5}$ .

$\frac{n^{5} m^{8}}{n^{7}}$

Cancel the common factors.

Factor $n^{5}$ out of $n^{7}$ .

$\frac{n^{5} m^{8}}{n^{5} n^{2}}$

Cancel the common factor.

$\frac{n^{5} m^{8}}{n^{5} n^{2}}$

Rewrite the expression.

$\frac{m^{8}}{n^{2}}$