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Simplify. Assume all variables are positive.\newlinez57⋅z127z^{\frac{5}{7}} \cdot z^{\frac{12}{7}}\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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Simplify expressions involving rational exponentsright chevron icon

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Q. Simplify. Assume all variables are positive.\newlinez57⋅z127z^{\frac{5}{7}} \cdot z^{\frac{12}{7}}\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 and Apply Exponent Rule: Identify the equation and apply the exponent rule for multiplication.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinez57×z127=z57+127z^{\frac{5}{7}} \times z^{\frac{12}{7}} = z^{\frac{5}{7} + \frac{12}{7}}.
  2. Add Exponents: Add the exponents.\newline57+127=(5+127)=177\frac{5}{7} + \frac{12}{7} = \left(\frac{5 + 12}{7}\right) = \frac{17}{7}.\newlineSo, z57⋅z127=z177z^{\frac{5}{7}} \cdot z^{\frac{12}{7}} = z^{\frac{17}{7}}.
  3. Write Final Answer: 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.\newlineThe final answer is z177z^{\frac{17}{7}}.

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