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Simplify. Assume all variables are positive.\newliner73r83r^{\frac{7}{3}} \cdot r^{\frac{8}{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.\newliner73r83r^{\frac{7}{3}} \cdot r^{\frac{8}{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 r7/3×r8/3r^{7/3} \times r^{8/3} and we need to simplify it.
  2. Apply product rule: Apply the product rule for exponents.\newlineThe product rule states that when multiplying like bases, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlineSo, r73×r83=r73+83r^{\frac{7}{3}} \times r^{\frac{8}{3}} = r^{\frac{7}{3} + \frac{8}{3}}.
  3. Perform addition: Perform the addition of the exponents.\newlineAdd the fractions 73\frac{7}{3} and 83\frac{8}{3}.\newline73+83=(7+8)3=153\frac{7}{3} + \frac{8}{3} = \frac{(7 + 8)}{3} = \frac{15}{3}.
  4. Simplify exponent: Simplify the exponent. \newline153\frac{15}{3} simplifies to 55.\newlineSo, r153=r5r^{\frac{15}{3}} = r^5.
  5. Write final answer: Write the final answer.\newlineThe simplified expression is r5r^5.

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