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Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{3}{4}}}{r^{\frac{5}{4}}}$ $\newline$ 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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Q. Simplify. Assume all variables are positive.

\newline

\frac{r^{\frac{3}{4}}}{r^{\frac{5}{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

______

Use Exponent Property: We have the expression $r^{\frac{3}{4}}/r^{\frac{5}{4}}$ . To simplify this, we will use the property of exponents that states when dividing like bases, we subtract the exponents.
Subtract Exponents: Subtract the exponents: $(\frac{3}{4}) - (\frac{5}{4})$ .
Perform Subtraction: Perform the subtraction: $(\frac{3}{4}) - (\frac{5}{4}) = -\frac{2}{4}$ .
Simplify Fraction: Simplify the fraction $-\frac{2}{4}$ to its simplest form, which is $-\frac{1}{2}$ .
Apply Exponent: Apply the simplified exponent to the base $r$ : $r^{(-\frac{1}{2})}$ .
Rewrite as Reciprocal: Since we assume all variables are positive and all exponents in the answer should be positive, we need to rewrite $r^{(-1/2)}$ as $1/r^{(1/2)}$ .
Recognize Square Root: Recognize that $r^{1/2}$ is the square root of $r$ , so the expression $1/r^{1/2}$ can also be written as $1/\sqrt{r}$ .

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