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Simplify. Assume all variables are positive.\newlinec12c12c^{\frac{1}{2}} \cdot c^{\frac{1}{2}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______

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Q. Simplify. Assume all variables are positive.\newlinec12c12c^{\frac{1}{2}} \cdot c^{\frac{1}{2}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
  1. Identify Equation and Apply Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: \newlineam×an=a(m+n)a^m \times a^n = a^{(m+n)}\newlineSo, c12×c12c^{\frac{1}{2}} \times c^{\frac{1}{2}} becomes c(12+12)c^{(\frac{1}{2} + \frac{1}{2})}.
  2. Add Exponents: Add the exponents.\newline12+12=1\frac{1}{2} + \frac{1}{2} = 1\newlineSo, c12+12c^{\frac{1}{2} + \frac{1}{2}} simplifies to c1c^1.
  3. Simplify Expression: Simplify the expression.\newlineAny number or variable to the power of 11 is itself, so c1c^1 is simply cc.

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