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Simplify. Assume all variables are positive.\newlinew17⋅w27w^{\frac{1}{7}} \cdot w^{\frac{2}{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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Full solution

Q. Simplify. Assume all variables are positive.\newlinew17⋅w27w^{\frac{1}{7}} \cdot w^{\frac{2}{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 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.\newlinew17×w27=w17+27w^{\frac{1}{7}} \times w^{\frac{2}{7}} = w^{\frac{1}{7} + \frac{2}{7}}
  2. Add Exponents: Add the exponents.\newline17+27=37\frac{1}{7} + \frac{2}{7} = \frac{3}{7}\newlineSo, w17×w27=w37w^{\frac{1}{7}} \times w^{\frac{2}{7}} = w^{\frac{3}{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 w37w^{\frac{3}{7}}, which is already in the correct form.

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