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

\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

Identify Expression: We have the expression: $v^{\frac{3}{2}}/v^{\frac{5}{2}}$ To simplify this expression, we need to subtract the exponents because we are dividing two powers with the same base.
Subtract Exponents: Subtract the exponents: $\newline$ $\frac{v^{\frac{3}{2}}}{v^{\frac{5}{2}}} = v^{\left(\frac{3}{2}-\frac{5}{2}\right)}$ $\newline$ Perform the subtraction: $\newline$ $= v^{-\frac{2}{2}}$ $\newline$ $= v^{-1}$
Perform Subtraction: Since we want the exponent to be positive, we rewrite the expression with a positive exponent: $\newline$ $v^{-1} = \frac{1}{v^{1}}$ $\newline$ This gives us the simplified form with a positive exponent.

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