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Simplify. Assume all variables are positive.\newlinet76t176t^{\frac{7}{6}} \cdot 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______

Full solution

Q. Simplify. Assume all variables are positive.\newlinet76t176t^{\frac{7}{6}} \cdot 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 and Apply Exponent Rule: 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}.\newlinet76×t176=t76+176t^{\frac{7}{6}} \times t^{\frac{17}{6}} = t^{\frac{7}{6} + \frac{17}{6}}.
  2. Add Exponents: Add the exponents. 76+176=246.\frac{7}{6} + \frac{17}{6} = \frac{24}{6}.
  3. Simplify Fraction: Simplify the fraction 24/624/6. 24/6=424/6 = 4.
  4. Write Final Answer: Write the final answer using the simplified exponent.\newlinet246=t4t^{\frac{24}{6}} = t^4.

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