Simplify. Assume all variables are positive. (u^(11/4))/(u^(11/4) * u^(5/4)) Write your answer in the form A or 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. ______

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

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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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Algebra 2

Simplify expressions involving rational exponents II

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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

\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: $\newline$ $a^{-m} = \frac{1}{a^m}$ $\newline$ $u^{-5/4} = \frac{1}{u^{5/4}}$