Question

simplify. assume all variables are positive.
$\frac{r^{\frac{1}{7}}}{r^{\frac{8}{7}}}$
write your answer in the form a or $\frac{a}{b}$, where a and b are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply exponent subtraction rule

$\frac{r^{\frac{1}{7}}}{r^{\frac{8}{7}}} = r^{\frac{1}{7}-\frac{8}{7}}$

Step2: Calculate the exponent

$r^{\frac{1-8}{7}} = r^{-\frac{7}{7}} = r^{-1}$

Step3: Rewrite to positive exponent

$r^{-1} = \frac{1}{r}$

Answer:

$\frac{1}{r}$