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Simplify. Assume all variables are positive. $\newline$ $\frac{d^{\frac{9}{4}}}{d^{\frac{7}{4}}}$ $\newline$ 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{7}{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

______

Given Expression: We have the expression: $\newline$ $d^{\frac{9}{4}} / d^{\frac{7}{4}}$ $\newline$ 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.
Exponent Operation: Subtract the exponents to combine the powers of $d$ into a single term: $\newline$ $d^{\frac{9}{4}} / d^{\frac{7}{4}} = d^{(\frac{9}{4} - \frac{7}{4})}$ $\newline$ Perform the subtraction: $\newline$ $d^{(\frac{9}{4} - \frac{7}{4})} = d^{\frac{2}{4}}$
Combine Powers: Simplify the exponent: $d^{\frac{2}{4}} = d^{\frac{1}{2}}$ This is because $\frac{2}{4}$ reduces to $\frac{1}{2}$ .
Simplify Exponent: We have now simplified the expression to: $d^{\frac{1}{2}}$ This is the final answer, and it is in the form $A$ or $\frac{A}{B}$ as requested, with $A$ being $d^{\frac{1}{2}}$ and no $B$ since there is no denominator.

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