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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{1}{4}}}{w^{\frac{7}{4}}}$ $\newline$ 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 II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{1}{4}}}{w^{\frac{7}{4}}}

\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

______

Write Power Division: Write $w^{\frac{1}{4}}/w^{\frac{7}{4}}$ as a single power of $w$ . $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $w^{\frac{1}{4}}/w^{\frac{7}{4}}$ $\newline$ = $w^{(\frac{1}{4})-(\frac{7}{4})}$ $\newline$ = $w^{-\frac{6}{4}}$
Simplify Exponent: Simplify the exponent. $w^{(-6/4)}$ can be simplified by reducing the fraction $-6/4$ to its simplest form. $w^{(-6/4)} = w^{(-3/2)}$
Express with Positive Exponent: Express $w^{-\frac{3}{2}}$ with a positive exponent. $\newline$ According to the negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^m}$ $\newline$ $w^{-\frac{3}{2}} = \frac{1}{w^{\frac{3}{2}}}$

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