Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{3}{5}}}{r^{\frac{9}{5}}}$ $\newline$ 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. $\newline$ ______ $\newline$

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{r^{\frac{3}{5}}}{r^{\frac{9}{5}}}

\newline

Write your answer in the form

A

\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.

\newline

______

\newline

Identify Expression: Identify the expression to simplify. $\newline$ We have the expression $r^{\frac{3}{5}} / r^{\frac{9}{5}}$ . To simplify an expression with exponents where the base is the same and we are dividing, we subtract the exponents.
Subtract Exponents: Subtract the exponents. $r^{\frac{3}{5}} / r^{\frac{9}{5}} = r^{\frac{3}{5} - \frac{9}{5}}$
Perform Subtraction: Perform the subtraction of the exponents. $\newline$ $\frac{3}{5} - \frac{9}{5} = -\frac{6}{5}$ $\newline$ So, $r^{\frac{3}{5}} / r^{\frac{9}{5}} = r^{-\frac{6}{5}}$
Rewrite Exponent: Since we want all exponents to be positive, we can rewrite $r^{(-6/5)}$ as $1/r^{(6/5)}$ .
Write Final Answer: Write the final answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ have no variables in common and all exponents are positive. $\newline$ The final answer is $\frac{1}{r^{\frac{6}{5}}}$ .