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Simplify. Assume all variables are positive.\newliney83y73y^{\frac{8}{3}} \cdot y^{\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.\newliney83y73y^{\frac{8}{3}} \cdot y^{\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 Equation and Apply Rule: Identify the equation and apply the exponent multiplication rule.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newliney83×y73=y83+73y^{\frac{8}{3}} \times y^{\frac{7}{3}} = y^{\frac{8}{3} + \frac{7}{3}}.
  2. Add Exponents: Add the exponents. 83+73=153\frac{8}{3} + \frac{7}{3} = \frac{15}{3}.
  3. Simplify Exponent: Simplify the exponent. 153=5\frac{15}{3} = 5.
  4. Write Final Answer: Write the final answer with the simplified exponent. y83×y73=y5y^{\frac{8}{3}} \times y^{\frac{7}{3}} = y^5.

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