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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}$ $\newline$ $\newline$ 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. $\newline$ ______ $\newline$

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Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\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

______

\newline

Apply rule for dividing powers: We are given the expression $(w^{\frac{3}{2}})/(w^{\frac{5}{2}})$ . To simplify this expression, we need to apply the rule for dividing powers with the same base, which states that we should subtract the exponents.
Perform subtraction of exponents: Perform the subtraction of the exponents: $(\frac{3}{2}) - (\frac{5}{2})$ . $\newline$ This gives us $w^{(\frac{3}{2}) - (\frac{5}{2})} = w^{(-\frac{2}{2})}$ .
Simplify the exponent: Simplify the exponent: $-\frac{2}{2}$ simplifies to $-1$ . $\newline$ So we have $w^{-1}$ .
Rewrite the expression: Since we want the exponent to be positive and the answer in the form $A$ or $\frac{A}{B}$ , we rewrite $w^{-1}$ as $\frac{1}{w^1}$ or simply $\frac{1}{w}$ .

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