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Simplify. Assume all variables are positive.\newlinec116⋅c136c^{\frac{11}{6}} \cdot c^{\frac{13}{6}}\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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Full solution

Q. Simplify. Assume all variables are positive.\newlinec116⋅c136c^{\frac{11}{6}} \cdot c^{\frac{13}{6}}\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 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/b)×c(c/d)=c((a/b)+(c/d))c^{(a/b)} \times c^{(c/d)} = c^{((a/b) + (c/d))}.
  2. Add Exponents: Add the exponents (116)(\frac{11}{6}) and (136):(\frac{13}{6}): (116)+(136)=(11+136)=246.(\frac{11}{6}) + (\frac{13}{6}) = (\frac{11 + 13}{6}) = \frac{24}{6}.
  3. Simplify Fraction: Simplify the fraction 246\frac{24}{6} to its lowest terms: 246=4\frac{24}{6} = 4.
  4. Write Final Answer: Write the final answer using the simplified exponent: c24/6=c4c^{24/6} = c^4.

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