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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. $\newline$ ______

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Simplify expressions involving rational exponents

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

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

______

Identify Equation and Apply Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: $a^m \times a^n = a^{m+n}$ . $\newline$ $y^{\frac{11}{6}} \times y^{\frac{11}{6}} = y^{\frac{11}{6} + \frac{11}{6}}$
Add Exponents: Add the exponents together. $\frac{11}{6} + \frac{11}{6} = \frac{22}{6}$
Simplify Exponent: Simplify the exponent by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $\frac{22}{6} = \left(\frac{22 \div 2}{6 \div 2}\right) = \frac{11}{3}$
Write Final Answer: Write the final answer with the simplified exponent. $y^{\frac{11}{3}}$

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