Simplify. Assume all variables are positive. $\newline$ $u^{\frac{7}{4}} \times u^{\frac{7}{4}}$ $\newline$ 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. $\newline$ ______

Full solution

Q. Simplify. Assume all variables are positive.

\newline

u^{\frac{7}{4}} \times u^{\frac{7}{4}}

\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 & Apply Rule: Identify the equation and apply the exponent multiplication rule. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $u^{\frac{7}{4}} \times u^{\frac{7}{4}} = u^{\frac{7}{4} + \frac{7}{4}}$ .
Perform Exponent Addition: Perform the addition of the exponents. $\frac{7}{4} + \frac{7}{4} = \frac{14}{4}.$
Simplify Exponent: Simplify the exponent. $\newline$ $\frac{14}{4}$ can be simplified to $3.5$ or $\frac{7}{2}$ (since $14$ divided by $4$ is $3$ with a remainder of $2$ , which gives us $3$ and $\frac{1}{2}$ or $\frac{7}{2}$ ). $\newline$ $3.5$ $0$ .
Write 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. $\newline$ The final answer is $u^{\frac{7}{2}}$ .