Simplify. Assume all variables are positive. $\newline$ $c^{\frac{11}{4}} \cdot c^{\frac{11}{4}}$ $\newline$ 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

c^{\frac{11}{4}} \cdot c^{\frac{11}{4}}

\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: Identify the equation and apply the property of exponents for multiplication. $\newline$ When multiplying two exponents with the same base, we add the exponents: $\newline$ $c^{\frac{a}{b}} \times c^{\frac{c}{d}} = c^{\left(\frac{a}{b} + \frac{c}{d}\right)}$ $\newline$ So, $c^{\frac{11}{4}} \times c^{\frac{11}{4}} = c^{\left(\frac{11}{4} + \frac{11}{4}\right)}$
Add Exponents: Add the exponents. $\newline$ $(\frac{11}{4}) + (\frac{11}{4}) = \frac{22}{4}$ $\newline$ So, $c^{(\frac{11}{4})} \cdot c^{(\frac{11}{4})} = c^{(\frac{22}{4})}$
Simplify Exponent: Simplify the exponent. $\newline$ $\frac{22}{4}$ can be simplified to $5.5$ or $\frac{11}{2}$ (since $\frac{22}{4}$ is $5$ with a remainder of $2$ , which gives us $5 \frac{2}{4}$ , and $\frac{2}{4}$ simplifies to $\frac{1}{2}$ ). $\newline$ So, $c^{\frac{22}{4}} = c^{\frac{11}{2}}$
Write Final Answer: Write the final answer in the form $A$ or $A/B$ . The final answer is $c^{11/2}$ , which is already in the form $A$ or $A/B$ , where $A$ is a constant or variable expression, and all exponents are positive.