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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. $\newline$ ______

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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

______

Identify Operation: Identify the operation to be applied with the exponents. $\newline$ When dividing powers with the same base, subtract the exponents.
Apply Operation: Apply the operation to the exponents. $\newline$ $\frac{v^{\frac{3}{2}}}{v^{\frac{5}{2}}} = v^{\left(\frac{3}{2} - \frac{5}{2}\right)} = v^{-\frac{2}{2}}$
Simplify Exponent: Simplify the exponent. $v^{(-2/2)} = v^{(-1)} = \frac{1}{v}$
Ensure Positivity: Ensure the exponent is positive. $\newline$ Since we assume all variables are positive, we can write the final answer with a positive exponent. $\newline$ $\frac{1}{v} = v^{-1}$

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