Simplify (m^7n^3)/(mn^-1)

$\frac{m^{7} n^{3}}{m n^{- 1}}$

Step 1

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

$\frac{m^{7} n^{3} n}{m}$

Step 2

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

Move $n$ .

$\frac{m^{7} (n \cdot n^{3})}{m}$

Multiply $n$ by $n^{3}$ .

Raise $n$ to the power of $1$ .

$\frac{m^{7} (n^{1} n^{3})}{m}$

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

$\frac{m^{7} n^{1 + 3}}{m}$

Add $1$ and $3$ .

$\frac{m^{7} n^{4}}{m}$

Step 3

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

Factor $m$ out of $m^{7} n^{4}$ .

$\frac{m (m^{6} n^{4})}{m}$

Cancel the common factors.

Raise $m$ to the power of $1$ .

$\frac{m (m^{6} n^{4})}{m^{1}}$

Factor $m$ out of $m^{1}$ .

$\frac{m (m^{6} n^{4})}{m \cdot 1}$

Cancel the common factor.

$\frac{m (m^{6} n^{4})}{m \cdot 1}$

Rewrite the expression.

$\frac{m^{6} n^{4}}{1}$

Divide $m^{6} n^{4}$ by $1$ .

$m^{6} n^{4}$