Simplify. Assume all variables are positive. $\newline$ $t^{\frac{8}{5}} \cdot t^{\frac{11}{5}}$ $\newline$ 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

t^{\frac{8}{5}} \cdot t^{\frac{11}{5}}

\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 and Apply Exponent Rule: Identify the equation and apply the exponent multiplication rule. $\newline$ When multiplying two exponents with the same base, we add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $t^{\frac{8}{5}} \times t^{\frac{11}{5}} = t^{\frac{8}{5} + \frac{11}{5}}$ .
Add Exponents: Add the exponents. $\newline$ $\frac{8}{5} + \frac{11}{5} = \left(8 + 11\right) / 5 = \frac{19}{5}$ . $\newline$ So, $t^{\frac{8}{5}} \times t^{\frac{11}{5}} = t^{\frac{19}{5}}$ .
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 $t^{\frac{19}{5}}$ , which is already in the correct form.