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Simplify. Assume all variables are positive.\newlineu43u73u^{\frac{4}{3}} \cdot u^{\frac{7}{3}}\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.\newlineu43u73u^{\frac{4}{3}} \cdot u^{\frac{7}{3}}\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}.\newlineu43×u73=u43+73u^{\frac{4}{3}} \times u^{\frac{7}{3}} = u^{\frac{4}{3} + \frac{7}{3}}.
  2. Add Exponents: Add the exponents.\newline43+73=(4+7)3\frac{4}{3} + \frac{7}{3} = \frac{(4 + 7)}{3}.
  3. Calculate Sum: Calculate the sum of the numerators.\newline4+7=114 + 7 = 11.
  4. Write Final Expression: Write the final expression with the combined exponent. u43×u73=u113u^{\frac{4}{3}} \times u^{\frac{7}{3}} = u^{\frac{11}{3}}.

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