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

Full solution

Q. Simplify. Assume all variables are positive.

\newline

u^{\frac{5}{2}} \cdot u^{\frac{5}{2}}

\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

______

Identify Equation: Identify the equation and apply the product of powers property. $\newline$ The product of powers property states that when you multiply two exponents with the same base, you add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ So, $u^{\frac{5}{2}} \times u^{\frac{5}{2}}$ can be simplified by adding the exponents.
Apply Property: Add the exponents. $\newline$ $u^{\frac{5}{2}} \times u^{\frac{5}{2}} = u^{\frac{5}{2} + \frac{5}{2}}$
Add Exponents: Perform the addition of the exponents. $\frac{5}{2} + \frac{5}{2} = \frac{10}{2}$
Perform Addition: Simplify the fraction $\frac{10}{2}$ . $\newline$ $\frac{10}{2} = 5$
Simplify Fraction: Write the final answer with the simplified exponent. $u^{\frac{5}{2}} \times u^{\frac{5}{2}} = u^5$