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Simplify. Assume all variables are positive.\newlinec73c23c^{\frac{7}{3}} \cdot c^{\frac{2}{3}}\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______

Full solution

Q. Simplify. Assume all variables are positive.\newlinec73c23c^{\frac{7}{3}} \cdot c^{\frac{2}{3}}\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: Identify the equation and apply the exponent rule for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinec73×c23=c73+23c^{\frac{7}{3}} \times c^{\frac{2}{3}} = c^{\frac{7}{3} + \frac{2}{3}}.
  2. Add Exponents: Add the exponents.\newline73+23=93\frac{7}{3} + \frac{2}{3} = \frac{9}{3}.
  3. Simplify Exponent: Simplify the exponent. 93=3\frac{9}{3} = 3.
  4. Write Final Answer: Write the final answer using the simplified exponent. c93=c3c^{\frac{9}{3}} = c^3.

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