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Simplify. Assume all variables are positive. $\newline$ $\frac{r^{\frac{3}{4}}}{r^{\frac{11}{4}}}$ $\newline$ 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{11}{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 $r^{\frac{3}{4}} / r^{\frac{11}{4}}$ . 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: $(\frac{3}{4}) - (\frac{11}{4})$ .
Perform Subtraction: Perform the subtraction: $(\frac{3}{4}) - (\frac{11}{4}) = -\frac{8}{4}$ .
Simplify Fraction: Simplify the fraction $-\frac{8}{4}$ to get $-2$ .
Convert to Positive Exponent: Now we have $r^{-2}$ , but we want the exponent to be positive. We can use the property of exponents that states a negative exponent means the reciprocal of the base raised to the positive exponent.
Convert to Positive Exponent: Now we have $r^{-2}$ , but we want the exponent to be positive. We can use the property of exponents that states a negative exponent means the reciprocal of the base raised to the positive exponent.Write $r^{-2}$ as $\frac{1}{r^2}$ to have a positive exponent.

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