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Simplify. Assume all variables are positive. $\newline$ $u^{\frac{5}{2}} \times u^{\frac{3}{2}}$ $\newline$ 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. $\newline$ ______

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Simplify expressions involving rational exponents II

Full solution

Q. Simplify. Assume all variables are positive.

\newline

u^{\frac{5}{2}} \times u^{\frac{3}{2}}

\newline

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.

\newline

______

Combine Exponents: Write $u^{\frac{5}{2}} \times u^{\frac{3}{2}}$ as a single power of $u$ . $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $u^{\frac{5}{2}} \times u^{\frac{3}{2}}$ $\newline$ = $u^{\left(\frac{5}{2}+\frac{3}{2}\right)}$ $\newline$ = $u^{\frac{8}{2}}$
Simplify Exponent: Simplify the exponent. $\newline$ $u^{\frac{8}{2}}$ $\newline$ = $u^4$
Final Answer: Write the final 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. $\newline$ Since we have $u^4$ , it is already in the correct form.

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