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Simplify. Assume all variables are positive.\newlineu136u176\frac{u^{\frac{13}{6}}}{u^{\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.\newlineu136u176\frac{u^{\frac{13}{6}}}{u^{\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 Expression: Identify the expression to simplify.\newlineWe have the expression u136/u176u^{\frac{13}{6}} / u^{\frac{17}{6}} and we need to simplify it.
  2. Apply Quotient Rule: Apply the quotient rule for exponents.\newlineThe quotient rule states that when dividing like bases with exponents, we subtract the exponents: am/an=a(mn)a^m / a^n = a^{(m-n)}.\newlineSo, u136/u176=u(136176)u^{\frac{13}{6}} / u^{\frac{17}{6}} = u^{(\frac{13}{6} - \frac{17}{6})}.
  3. Perform Subtraction: Perform the subtraction of the exponents.\newlineCalculate 136176=46\frac{13}{6} - \frac{17}{6} = -\frac{4}{6}.
  4. Simplify Fraction: Simplify the fraction 46-\frac{4}{6}. The fraction 46-\frac{4}{6} can be simplified to 23-\frac{2}{3} by dividing both the numerator and the denominator by 22.
  5. Write Final Answer: Write the final answer with a positive exponent.\newlineSince we cannot have negative exponents in the final answer, we express u2/3u^{-2/3} as 1/u2/31/u^{2/3}.

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