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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{1}{2}}}{s^{\frac{3}{2}}}$ $\newline$ 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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Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

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

______

Apply Exponent Rule: We have the expression: $\newline$ $s^{\frac{1}{2}}/s^{\frac{3}{2}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted. $\newline$ So, we will use the subtraction operation with the exponents.
Subtract Exponents: Subtract the exponents of $s$ : $s^{1/2}/s^{3/2} = s^{(1/2)-(3/2)}$ Perform the subtraction: $= s^{-2/2} = s^{-1}$
Rewrite Negative Exponent: Since we want the exponent to be positive, we rewrite $s^{-1}$ as: $\newline$ $s^{-1} = \frac{1}{s^{1}}$ $\newline$ This gives us the expression with a positive exponent.

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