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Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{3}{4}}}{r^{\frac{9}{4}}}$ $\newline$ 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}{4}}}{r^{\frac{9}{4}}}

\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: $\newline$ $r^{\frac{3}{4}}/r^{\frac{9}{4}}$ $\newline$ Which operation will be applied with exponent? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Subtract Exponents: Simplify the expression by subtracting the exponents. $\newline$ $r^{\frac{3}{4}}/r^{\frac{9}{4}}$ $\newline$ = $r^{\frac{3}{4} - \frac{9}{4}}$ $\newline$ = $r^{-\frac{6}{4}}$
Convert Negative Exponent: Simplify the negative exponent by writing it as a positive exponent in the denominator. $\newline$ $r^{(-\frac{6}{4})}$ $\newline$ = $\frac{1}{r^{(\frac{6}{4})}}$
Simplify Fraction: Simplify the fraction in the exponent. $\newline$ $\frac{1}{r^{\frac{6}{4}}}$ $\newline$ = $\frac{1}{r^{\frac{3}{2}}}$

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