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Simplify. Assume all variables are positive. $\newline$ $\frac{u^{\frac{11}{4}}}{u^{\frac{11}{4}} \cdot u^{\frac{5}{4}}}$ $\newline$ $\newline$ 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{u^{\frac{11}{4}}}{u^{\frac{11}{4}} \cdot u^{\frac{5}{4}}}

\newline

\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

______

Combine powers of $\newline$ $u$ : Combine the powers of $\newline$ $u$ in the denominator. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $\newline$ $u^{11/4} \times u^{5/4}$ $\newline$ = $\newline$ $u^{(11/4) + (5/4)}$ $\newline$ = $\newline$ $u^{16/4}$ $\newline$ = $\newline$ $u^4$
Divide powers of u: Divide the power of $u$ in the numerator by the power of $u$ in the denominator. $\newline$ When dividing powers with the same base, we subtract the exponents. $\newline$ $u^{11/4} / u^4$ $\newline$ = $u^{(11/4) - 4}$ $\newline$ = $u^{(11/4) - (16/4)}$ $\newline$ = $u^{-5/4}$
Express $u$ with positive exponent: Express $u^{-5/4}$ with a positive exponent. $\newline$ According to the negative exponent rule: $\newline$ $a^{-m} = \frac{1}{a^m}$ $\newline$ $u^{-5/4} = \frac{1}{u^{5/4}}$

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