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Simplify. Assume all variables are positive. $\newline$ $\frac{u^{\frac{4}{3}}}{u^{\frac{5}{3}}}$ $\newline$ 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{4}{3}}}{u^{\frac{5}{3}}}

\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 with exponents: We have the expression: $\newline$ $u^{\frac{4}{3}}/u^{\frac{5}{3}}$ $\newline$ 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: $\newline$ $u^{\frac{4}{3}}/u^{\frac{5}{3}}$ $\newline$ = $u^{\frac{4}{3} - \frac{5}{3}}$ $\newline$ = $u^{-\frac{1}{3}}$
Apply property of negative exponents: Since we want the exponent to be positive, we can rewrite the expression using the property of negative exponents, which states that $a^{-n} = \frac{1}{a^n}$ : $\newline$ $u^{-\frac{1}{3}} = \frac{1}{u^{\frac{1}{3}}}$

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