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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{1}{2}}}{w^{\frac{3}{2}}}$ $\newline$ 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 expressions involving rational exponents

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{1}{2}}}{w^{\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

______

Identify Operation: We have the expression: $\newline$ $w^{\frac{1}{2}} / w^{\frac{3}{2}}$ $\newline$ Which operation will be applied with the exponents? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Subtract Exponents: Now, let's simplify the expression by subtracting the exponents: $\newline$ $w^{\frac{1}{2}} / w^{\frac{3}{2}}$ $\newline$ = $w^{\frac{1}{2} - \frac{3}{2}}$ $\newline$ = $w^{-\frac{2}{2}}$ $\newline$ = $w^{-1}$ $\newline$ However, we want the exponent to be positive, as per the instructions.
Simplify Expression: To make the exponent positive, we can take the reciprocal of the base: $\newline$ $w^{-1} = \frac{1}{w^1} = \frac{1}{w}$ $\newline$ Now the exponent is positive, and the expression is simplified.

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