Simplify. Assume all variables are positive. $\newline$ $u^{\frac{1}{3}} \cdot u^{\frac{1}{3}}$ $\newline$ 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{1}{3}} \cdot u^{\frac{1}{3}}

\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 Expression: Identify the expression to be simplified. $\newline$ We have the expression $u^{\frac{1}{3}} \times u^{\frac{1}{3}}$ , which involves multiplying two powers of the same base $u$ .
Apply Product Rule: Apply the product rule for exponents. $\newline$ The product rule states that when multiplying two powers with the same base, you add the exponents: $a^m \times a^n = a^{(m+n)}$ . $\newline$ So, $u^{\frac{1}{3}} \times u^{\frac{1}{3}} = u^{(\frac{1}{3} + \frac{1}{3})}$ .
Perform Exponent Addition: Perform the addition of the exponents. $\newline$ Add the exponents $\frac{1}{3}$ and $\frac{1}{3}$ . $\newline$ $\frac{1}{3} + \frac{1}{3} = \frac{2}{3}$ . $\newline$ So, $u^{\frac{1}{3}} * u^{\frac{1}{3}} = u^{\frac{2}{3}}$ .
Write Final Expression: Write the final simplified expression. $\newline$ The expression $u^{\frac{1}{3}} \times u^{\frac{1}{3}}$ simplifies to $u^{\frac{2}{3}}$ .