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Simplify. Assume all variables are positive. $\newline$ $\frac{d^{\frac{9}{4}}}{d^{\frac{5}{4}}}$ $\newline$ 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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Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{d^{\frac{9}{4}}}{d^{\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

______

Identify Operation: We have the expression: $\newline$ $d^{\frac{9}{4}} / d^{\frac{5}{4}}$ $\newline$ What operation will be applied with the exponents? $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ So, we will use the subtraction operation with the exponents.
Combine Powers: Subtract the exponents to combine the powers of $d$ : $d^{\frac{9}{4}} / d^{\frac{5}{4}} = d^{(\frac{9}{4}) - (\frac{5}{4})}$ Perform the subtraction: $d^{(\frac{9}{4}) - (\frac{5}{4})} = d^{\frac{4}{4}}$ $d^{\frac{4}{4}} = d^1$
Simplify Expression: Simplify the expression: $\newline$ Since $d^1$ is simply $d$ , the final simplified form is: $\newline$ $d$

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