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Simplify. Assume all variables are positive. $\newline$ $\frac{u^{\frac{3}{4}}}{u^{\frac{7}{4}}}$ $\newline$ 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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

\frac{u^{\frac{3}{4}}}{u^{\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

______

Identify Expression: We have the expression: $\newline$ $\frac{u^{\frac{3}{4}}}{u^{\frac{7}{4}}}$ $\newline$ Which operation will be applied with exponent? $\newline$ When dividing powers with the same base, the exponents are subtracted.
Apply Rule for Dividing Exponents: Apply the rule for dividing exponents with the same base: $u^{\frac{3}{4}}/u^{\frac{7}{4}} = u^{\frac{3}{4} - \frac{7}{4}}$ Perform the subtraction of the exponents. $u^{-\frac{4}{4}}$
Simplify Exponent: Simplify the exponent: $u^{(-4/4)} = u^{(-1)}$ Since we want the exponent to be positive, we can rewrite the expression using the property of negative exponents. $u^{(-1)} = \frac{1}{u}$

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