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Simplify. Assume all variables are positive.\newlinew47⋅w67w^{\frac{4}{7}} \cdot w^{\frac{6}{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.\newlinew47⋅w67w^{\frac{4}{7}} \cdot w^{\frac{6}{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 Property: Identify the equation and apply the property of exponents for multiplication, which states that when multiplying like bases, you add the exponents: w(a/b)×w(c/d)=w((a/b)+(c/d))w^{(a/b)} \times w^{(c/d)} = w^{((a/b) + (c/d))}.
  2. Add Exponents: Add the exponents (47)(\frac{4}{7}) and (67)(\frac{6}{7}): (47)+(67)=(4+67)=107(\frac{4}{7}) + (\frac{6}{7}) = (\frac{4+6}{7}) = \frac{10}{7}.
  3. Write Final Expression: Write the final expression using the sum of the exponents: w107w^{\frac{10}{7}}.
  4. Check Exponent Form: Check that the final expression has a positive exponent and that it is in the simplest form.

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