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Simplify. Assume all variables are positive.\newlineu67×u127u^{\frac{6}{7}} \times u^{\frac{12}{7}}\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.\newlineu67×u127u^{\frac{6}{7}} \times u^{\frac{12}{7}}\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 & Apply Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying powers with the same base, we add the exponents: \newlineua×ub=u(a+b)u^a \times u^b = u^{(a+b)}\newlineu67×u127u^{\frac{6}{7}} \times u^{\frac{12}{7}} can be simplified by adding the exponents.
  2. Add Exponents: Add the exponents (67)(\frac{6}{7}) and (127)(\frac{12}{7}).\newlineu(67+127)=u187u^{(\frac{6}{7} + \frac{12}{7})} = u^{\frac{18}{7}}
  3. Write Final Answer: Write the final 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.\newlineThe final answer is u187u^{\frac{18}{7}}, which is already in the correct form.

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