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Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{11}{4}}}{r^{\frac{9}{4}}}$ $\newline$ 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{11}{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

______

Apply operation with exponent: We have the expression: $\newline$ $r^{\frac{11}{4}} / r^{\frac{9}{4}}$ $\newline$ Which operation will be applied with exponent? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Simplify by subtracting exponents: We simplify the expression by subtracting the exponents: $r^{\frac{11}{4}} / r^{\frac{9}{4}} = r^{\frac{11}{4} - \frac{9}{4}} = r^{\frac{2}{4}}$
Further reduce the exponent: We can further simplify the exponent by reducing the fraction $\frac{2}{4}$ to its simplest form: $r^{\frac{2}{4}} = r^{\frac{1}{2}}$

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