Simplify. Assume all variables are positive. $\newline$ $t^{\frac{7}{6}} \cdot t^{\frac{13}{6}}$ $\newline$ 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{7}{6}} \cdot t^{\frac{13}{6}}

\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: $a^m \times a^n = a^{m+n}$ . $\newline$ $t^{\frac{7}{6}} \times t^{\frac{13}{6}} = t^{\frac{7}{6} + \frac{13}{6}}$ .
Add Exponents: Add the exponents. $\frac{7}{6} + \frac{13}{6} = \left(\frac{7 + 13}{6}\right) = \frac{20}{6}.$
Simplify Fraction: Simplify the fraction $\frac{20}{6}$ . $\frac{20}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\frac{20}{6} = \frac{(20/2)}{(6/2)} = \frac{10}{3}$ .
Write Final Answer: Write the final answer using the simplified exponent. $\newline$ $t^{\frac{7}{6}} \times t^{\frac{13}{6}} = t^{\frac{20}{6}} = t^{\frac{10}{3}}$ .