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Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{3}{2}}}{r^{\frac{5}{2}}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{r^{\frac{3}{2}}}{r^{\frac{5}{2}}}

\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

______

Identify operation: We have the expression: $\newline$ $r^{\frac{3}{2}} / r^{\frac{5}{2}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Apply rule for dividing exponents: Simplify the expression using the rule for dividing exponents with the same base: $r^{\frac{3}{2}} / r^{\frac{5}{2}} = r^{\frac{3}{2} - \frac{5}{2}} = r^{-\frac{2}{2}} = r^{-1}$ . Since we want the exponent to be positive, we can rewrite $r^{-1}$ as $\frac{1}{r}$ .
Simplify using rule: The final simplified expression is: $\newline$ $\frac{1}{r}$ $\newline$ This is already in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ have no variables in common, and all exponents are positive.

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