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Simplify. Assume all variables are positive.\newlinet116×t176t^{\frac{11}{6}} \times t^{\frac{17}{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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Q. Simplify. Assume all variables are positive.\newlinet116×t176t^{\frac{11}{6}} \times t^{\frac{17}{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 and Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: \newlinetab×tcd=t(ab+cd)t^{\frac{a}{b}} \times t^{\frac{c}{d}} = t^{\left(\frac{a}{b} + \frac{c}{d}\right)}
  2. Add Exponents: Add the exponents (116)(\frac{11}{6}) and (176)(\frac{17}{6}).116+176=11+176\frac{11}{6} + \frac{17}{6} = \frac{11 + 17}{6}
  3. Perform Addition: Perform the addition in the numerator. 11+17=2811 + 17 = 28
  4. Write Single Exponent: Write the result as a single exponent.\newlinet286t^{\frac{28}{6}}
  5. Simplify Fraction: Simplify the fraction 286\frac{28}{6}. 286\frac{28}{6} can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 22. 28÷2=1428 \div 2 = 14 6÷2=36 \div 2 = 3
  6. Write Simplified Exponent: Write the simplified exponent. t143t^{\frac{14}{3}}

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