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Simplify. Assume all variables are positive. $\newline$ $\frac{v^{5/2}}{v^{5/2} \cdot v^{1/2}}$ $\newline$ Write your answer in the form $A$ or $A/B$ , 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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Multiplication with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{v^{5/2}}{v^{5/2} \cdot v^{1/2}}

\newline

Write your answer in the form

A

or

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

______

Write Expression: Write down the expression to be simplified. $\newline$ $\frac{v^{5/2}}{v^{5/2} \cdot v^{1/2}}$
Apply Exponent Property: Apply the property of exponents that states when dividing like bases, you subtract the exponents. $\newline$ $v^{\frac{5}{2}} / (v^{\frac{5}{2}} \cdot v^{\frac{1}{2}}) = v^{\frac{5}{2}} / v^{\frac{5}{2} + \frac{1}{2}}$
Add Exponents: Add the exponents in the denominator. $\newline$ $v^{\frac{5}{2}} / v^{\frac{5}{2} + \frac{1}{2}} = v^{\frac{5}{2}} / v^{\frac{6}{2}}$
Simplify Denominator: Simplify the exponent in the denominator. $\newline$ $\frac{v^{5/2}}{v^{6/2}} = \frac{v^{5/2}}{v^3}$
Subtract Exponents: Subtract the exponents $\frac{5}{2} - 3 = \frac{5}{2} - \frac{6}{2}$ . $v^{\frac{5}{2}} / v^3 = v^{\frac{5}{2} - \frac{6}{2}} = v^{-\frac{1}{2}}$
Rewrite Negative Exponent: Since we want all exponents to be positive, we can rewrite the expression with a positive exponent by using the property that $x^{-n} = \frac{1}{x^n}$ . $\newline$ $v^{-\frac{1}{2}} = \frac{1}{v^{\frac{1}{2}}}$
Final Simplification: Simplify the expression. $\newline$ $\frac{1}{v^{\frac{1}{2}}}$ is already in the simplest form.

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