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Simplify. Assume all variables are positive.\newlinez34z54z^{\frac{3}{4}} \cdot z^{\frac{5}{4}}\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.\newlinez34z54z^{\frac{3}{4}} \cdot z^{\frac{5}{4}}\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 Property: Identify the equation and apply the property of exponents for multiplication.\newlineWhen multiplying powers with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinez34×z54=z34+54z^{\frac{3}{4}} \times z^{\frac{5}{4}} = z^{\frac{3}{4} + \frac{5}{4}}.
  2. Add Exponents: Add the exponents. 34+54=84\frac{3}{4} + \frac{5}{4} = \frac{8}{4}.
  3. Simplify Fraction: Simplify the fraction 8/48/4. 8/4=28/4 = 2.
  4. Write Final Answer: Write the final answer using the simplified exponent. z34×z54=z2z^{\frac{3}{4}} \times z^{\frac{5}{4}} = z^2.

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