Simplify. Assume all variables are positive. $\newline$ $y^{\frac{11}{6}} \cdot y^{\frac{11}{6}}$ $\newline$ 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

y^{\frac{11}{6}} \cdot y^{\frac{11}{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 Property: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying two expressions with the same base, we add the exponents. $\newline$ $y^{\frac{11}{6}} \times y^{\frac{11}{6}} = y^{\frac{11}{6} + \frac{11}{6}}$
Add Exponents: Add the exponents. $\newline$ $\frac{11}{6} + \frac{11}{6} = \frac{22}{6}$ $\newline$ So, $y^{\frac{11}{6}} \times y^{\frac{11}{6}} = y^{\frac{22}{6}}$
Simplify Exponent: Simplify the exponent. $\newline$ $\frac{22}{6}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{22}{6} \div \frac{2}{2} = \frac{11}{3}$ $\newline$ So, $y^{\frac{22}{6}} = y^{\frac{11}{3}}$
Write Final Answer: Write the final answer. $\newline$ The simplified form of $y^{\frac{11}{6}} \times y^{\frac{11}{6}}$ is $y^{\frac{11}{3}}$ .