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Simplify. Assume all variables are positive.\newliner43×r73r^{\frac{4}{3}} \times r^{\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______

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Q. Simplify. Assume all variables are positive.\newliner43×r73r^{\frac{4}{3}} \times r^{\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 Expression: Identify the expression to be simplified.\newlineWe have the expression r4/3×r7/3r^{4/3} \times r^{7/3} and we need to simplify it.
  2. Apply Product Rule: Apply the product rule for exponents.\newlineThe product rule states that when multiplying two powers with the same base, you add the exponents. So, we add the exponents 43\frac{4}{3} and 73\frac{7}{3}.\newliner43×r73=r43+73r^{\frac{4}{3}} \times r^{\frac{7}{3}} = r^{\frac{4}{3} + \frac{7}{3}}
  3. Perform Exponent Addition: Perform the addition of the exponents.\newlineAdd the fractions 43\frac{4}{3} and 73\frac{7}{3}.\newline43+73=(4+7)3\frac{4}{3} + \frac{7}{3} = \frac{(4 + 7)}{3}\newline43+73=113\frac{4}{3} + \frac{7}{3} = \frac{11}{3}
  4. Write Final Expression: Write the final simplified expression.\newlineThe expression r43×r73r^{\frac{4}{3}} \times r^{\frac{7}{3}} simplifies to r113r^{\frac{11}{3}}.

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