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Simplify. Assume all variables are positive.\newliney17⋅y47y^{\frac{1}{7}} \cdot y^{\frac{4}{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.\newliney17⋅y47y^{\frac{1}{7}} \cdot y^{\frac{4}{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: ya×yb=ya+by^{a} \times y^{b} = y^{a+b}.
  2. Add Exponents: Add the exponents 17\frac{1}{7} and 47\frac{4}{7} together: (17)+(47)=57\left(\frac{1}{7}\right) + \left(\frac{4}{7}\right) = \frac{5}{7}.
  3. Write Simplified Expression: Write the simplified expression using the sum of the exponents: y17×y47=y57y^{\frac{1}{7}} \times y^{\frac{4}{7}} = y^{\frac{5}{7}}.
  4. Check Final Expression: Check that the final expression has a positive exponent and that there are no variables in common in the numerator and denominator, which is true since the expression is y57y^{\frac{5}{7}}.

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