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Simplify. Assume all variables are positive.\newlinex45×x145x^{\frac{4}{5}} \times x^{\frac{14}{5}}\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.\newlinex45×x145x^{\frac{4}{5}} \times x^{\frac{14}{5}}\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 two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinex45×x145=x45+145x^{\frac{4}{5}} \times x^{\frac{14}{5}} = x^{\frac{4}{5} + \frac{14}{5}}.
  2. Add Exponents: Add the exponents.\newline45+145=(4+14)5\frac{4}{5} + \frac{14}{5} = \frac{(4 + 14)}{5}.
  3. Perform Addition: Perform the addition.\newline(4+14)/5=18/5(4 + 14) / 5 = 18/5.
  4. Write Final Expression: Write the final expression using the sum of the exponents. x45×x145=x185x^{\frac{4}{5}} \times x^{\frac{14}{5}} = x^{\frac{18}{5}}.

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