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Simplify. Assume all variables are positive.\newlinez23×z53z^{\frac{2}{3}} \times z^{\frac{5}{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.\newlinez23×z53z^{\frac{2}{3}} \times z^{\frac{5}{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: Identify the equation and apply the product of powers property.\newlineThe product of powers property states that when you multiply two powers with the same base, you add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlineSo, z23×z53z^{\frac{2}{3}} \times z^{\frac{5}{3}} can be simplified by adding the exponents.
  2. Apply Product of Powers: Add the exponents (23)(\frac{2}{3}) and (53)(\frac{5}{3}).(23)+(53)=(2+53)=73(\frac{2}{3}) + (\frac{5}{3}) = (\frac{2+5}{3}) = \frac{7}{3}So, z(23)∗z(53)=z(73)z^{(\frac{2}{3})} * z^{(\frac{5}{3})} = z^{(\frac{7}{3})}.
  3. Add Exponents: Write the final 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.\newlineSince z73z^{\frac{7}{3}} is already in the correct form with a positive exponent, this is our final answer.

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