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Simplify. Assume all variables are positive. $\newline$ $c^{\frac{1}{2}} \cdot c^{\frac{5}{2}}$ $\newline$ 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

c^{\frac{1}{2}} \cdot c^{\frac{5}{2}}

\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 Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: $c^a \times c^b = c^{a+b}$ .
Add Exponents: Perform the addition of the exponents: $(\frac{1}{2}) + (\frac{5}{2})$ .
Calculate Sum: Calculate the sum of the exponents: $(\frac{1}{2}) + (\frac{5}{2}) = \frac{1+5}{2} = \frac{6}{2}$ .
Simplify Fraction: Simplify the fraction $\frac{6}{2}$ to get the final exponent for $c$ .
Final Exponent: The simplified fraction is $\frac{6}{2} = 3$ , so the final exponent for $c$ is $3$ .
Write Final Expression: Write the final simplified expression using the exponent calculated: $c^3$ .

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