Simplify. Assume all variables are positive. $\newline$ $x^{\frac{7}{3}} \times x^{\frac{1}{3}}$ $\newline$ 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

x^{\frac{7}{3}} \times x^{\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 Equation and Apply Property: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $x^{\frac{7}{3}} \times x^{\frac{1}{3}} = x^{\frac{7}{3} + \frac{1}{3}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{7}{3} + \frac{1}{3} = \frac{8}{3}$ . $\newline$ So, $x^{\frac{7}{3}} \times x^{\frac{1}{3}} = x^{\frac{8}{3}}$ .
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 $x^{\frac{8}{3}}$ , which is already in the correct form.