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Simplify. Assume all variables are positive.\newlineb25b145b^{\frac{2}{5}} \cdot b^{\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.\newlineb25b145b^{\frac{2}{5}} \cdot b^{\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: \newlinebm×bn=bm+nb^m \times b^n = b^{m+n}\newlineSo, b25×b145b^{\frac{2}{5}} \times b^{\frac{14}{5}} becomes b25+145b^{\frac{2}{5} + \frac{14}{5}}.
  2. Add Exponents: Add the exponents. 25+145\frac{2}{5} + \frac{14}{5} equals 165\frac{16}{5} when we add the numerators and keep the denominator the same.
  3. Write Final Expression: Write the final expression using the sum of the exponents. b2/5×b14/5b^{2/5} \times b^{14/5} simplifies to b16/5b^{16/5}.

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