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Simplify. Assume all variables are positive. $\newline$ $\frac{u^{\frac{11}{4}}}{u^{\frac{7}{4}} \cdot u^{\frac{5}{4}}}$ $\newline$ 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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Q. Simplify. Assume all variables are positive.

\newline

\frac{u^{\frac{11}{4}}}{u^{\frac{7}{4}} \cdot u^{\frac{5}{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

______

Use Exponent Properties: We have the expression: $u^{\frac{11}{4}} / (u^{\frac{7}{4}} * u^{\frac{5}{4}})$ $\newline$ First, let's use the property of exponents that states $(a^m)/(a^n) = a^{m-n}$ and $a^m * a^n = a^{m+n}$ .
Combine Exponents in Denominator: Combine the exponents in the denominator using the multiplication property of exponents: $u^{\frac{7}{4}} \times u^{\frac{5}{4}} = u^{\frac{7}{4} + \frac{5}{4}}$ .
Calculate Sum of Exponents: Calculate the sum of the exponents in the denominator: $\frac{7}{4} + \frac{5}{4} = \frac{12}{4}$ .
Simplify Exponents: Simplify the sum of the exponents in the denominator: $\frac{12}{4} = 3$ . So, $u^{\frac{7}{4}} \times u^{\frac{5}{4}} = u^3$ .
Divide Exponents: Now, divide the exponents using the division property of exponents: $u^{\frac{11}{4}} / u^3 = u^{\frac{11}{4} - 3}$ .
Convert Whole Number to Fraction: Convert the whole number $3$ to a fraction with the same denominator as $\frac{11}{4}$ to subtract the exponents: $3 = \frac{12}{4}$ .
Subtract Exponents: Subtract the exponents: $\frac{11}{4} - \frac{12}{4} = -\frac{1}{4}$ .
Write Positive Exponent: Since we assume all variables are positive and we want the exponent to be positive, we can write $u^{-\frac{1}{4}}$ as $\frac{1}{u^{\frac{1}{4}}}$ .

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