Simplify (r^6n^-7)/(r^4n^2)

$\frac{r^{6} n^{- 7}}{r^{4} n^{2}}$

Step 1

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

$\frac{r^{6}}{r^{4} n^{2} n^{7}}$

Step 2

Multiply $n^{2}$ by $n^{7}$ by adding the exponents.

Move $n^{7}$ .

$\frac{r^{6}}{r^{4} (n^{7} n^{2})}$

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

$\frac{r^{6}}{r^{4} n^{7 + 2}}$

Add $7$ and $2$ .

$\frac{r^{6}}{r^{4} n^{9}}$

Step 3

Cancel the common factor of $r^{6}$ and $r^{4}$ .

Factor $r^{4}$ out of $r^{6}$ .

$\frac{r^{4} r^{2}}{r^{4} n^{9}}$

Cancel the common factors.

Factor $r^{4}$ out of $r^{4} n^{9}$ .

$\frac{r^{4} r^{2}}{r^{4} (n^{9})}$

Cancel the common factor.

$\frac{r^{4} r^{2}}{r^{4} n^{9}}$

Rewrite the expression.

$\frac{r^{2}}{n^{9}}$