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Simplify. Assume all variables are positive.\newliner13r43r^{\frac{1}{3}} \cdot r^{\frac{4}{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.\newliner13r43r^{\frac{1}{3}} \cdot r^{\frac{4}{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 simplify.\newlineWe have the expression r1/3×r4/3r^{1/3} \times r^{4/3} 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 13\frac{1}{3} and 43\frac{4}{3}.\newliner13×r43=r13+43r^{\frac{1}{3}} \times r^{\frac{4}{3}} = r^{\frac{1}{3} + \frac{4}{3}}
  3. Perform addition: Perform the addition of the exponents.\newline13+43=53\frac{1}{3} + \frac{4}{3} = \frac{5}{3}\newlineSo, r13×r43=r53r^{\frac{1}{3}} \times r^{\frac{4}{3}} = r^{\frac{5}{3}}
  4. Write final expression: Write the final simplified expression.\newlineThe expression r1/3×r4/3r^{1/3} \times r^{4/3} simplifies to r5/3r^{5/3}.

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