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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{1}{2}}}{s^{\frac{3}{2}} \cdot s^{\frac{3}{2}}}$ $\newline$ 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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Simplify radical expressions with variables II

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Q. Simplify. Assume all variables are positive.

\newline

\frac{s^{\frac{1}{2}}}{s^{\frac{3}{2}} \cdot s^{\frac{3}{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

______

Use Exponent Properties: We are given the expression $s^{\frac{1}{2}}/(s^{\frac{3}{2}} * s^{\frac{3}{2}})$ . To simplify this expression, we will use the properties of exponents.
Combine Denominator Exponents: First, let's combine the exponents in the denominator using the property of exponents that states $a^{m} \times a^{n} = a^{m+n}$ . So, $s^{\frac{3}{2}} \times s^{\frac{3}{2}} = s^{\frac{3}{2} + \frac{3}{2}} = s^{\frac{6}{2}} = s^3$ .
Subtract Exponents: Now we have the expression $s^{1/2}/s^3$ . We can simplify this by subtracting the exponents in the numerator from the exponents in the denominator using the property $a^{m}/a^{n} = a^{m-n}$ . So, $s^{1/2}/s^3 = s^{1/2 - 3} = s^{1/2 - 6/2} = s^{-5/2}$ .
Final Simplification: Since we want the exponent to be positive and we are assuming all variables are positive, we can write $s^{(-5/2)}$ as $1/s^{(5/2)}$ .

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