Simplify. Assume all variables are positive. $\newline$ $d^{\frac{4}{3}} \cdot d^{\frac{1}{3}}$ $\newline$ 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

d^{\frac{4}{3}} \cdot d^{\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 & Apply Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: $a^m \times a^n = a^{m+n}$ . $d^{\frac{4}{3}} \times d^{\frac{1}{3}} = d^{\frac{4}{3} + \frac{1}{3}}$
Perform Exponent Addition: Perform the addition of the exponents. $\frac{4}{3} + \frac{1}{3} = \frac{5}{3}$
Write Final Simplified Expression: Write the final simplified expression using the sum of the exponents. $d^{\frac{4}{3}} \times d^{\frac{1}{3}} = d^{\frac{5}{3}}$
Check Exponent & Simplify: Check that the final expression has a positive exponent and is in the simplest form. $\newline$ The exponent $\frac{5}{3}$ is positive, and the expression cannot be simplified further.