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Simplify. Assume all variables are positive. $\newline$ $\frac{w^{\frac{3}{4}}}{w^{\frac{11}{4}}}$ $\newline$ 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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{4}}}{w^{\frac{11}{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

______

Apply Exponent Rule: We have the expression: $w^{\frac{3}{4}}/w^{\frac{11}{4}}$ Which operation will be applied with the exponents? When dividing powers with the same base, the exponents are subtracted.
Simplify Expression: Apply the exponent rule for division: $\newline$ $w^{\frac{3}{4}}/w^{\frac{11}{4}}$ $\newline$ Simplify the expression by subtracting the exponents. $\newline$ $w^{\frac{3}{4} - \frac{11}{4}}$ $\newline$ $w^{-\frac{8}{4}}$ $\newline$ $w^{-2}$
Use Negative Exponents: Since we need to write the answer with a positive exponent, we can rewrite the expression using the property of negative exponents: $\newline$ $w^{-2} = \frac{1}{w^2}$

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