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Simplify. Assume all variables are positive. $\newline$ $\frac{s^{\frac{9}{4}}}{s^{\frac{11}{4}}}$ $\newline$ 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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Division with rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{s^{\frac{9}{4}}}{s^{\frac{11}{4}}}

\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

______

Identify the expression: We have the expression: $\newline$ $s^{\frac{9}{4}} / s^{\frac{11}{4}}$ $\newline$ 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.
Apply subtraction operation: Subtract the exponents of $s$ : $\frac{s^{9/4}}{s^{11/4}} = s^{(9/4) - (11/4)}$ Perform the subtraction: $s^{(9/4) - (11/4)} = s^{-2/4}$ Simplify the exponent: $s^{-2/4} = s^{-1/2}$
Perform exponent subtraction: Simplify the expression with a negative exponent: $\newline$ $s^{-\frac{1}{2}}$ $\newline$ According to the rules of exponents, a negative exponent indicates the reciprocal of the base raised to the positive exponent. $\newline$ So, $s^{-\frac{1}{2}} = \frac{1}{s^{\frac{1}{2}}}$

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