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Simplify. Assume all variables are positive.\newlineb65b75b^{\frac{6}{5}} \cdot b^{\frac{7}{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.\newlineb65b75b^{\frac{6}{5}} \cdot b^{\frac{7}{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 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: \newlinebmn×bpq=bmn+pqb^{\frac{m}{n}} \times b^{\frac{p}{q}} = b^{\frac{m}{n} + \frac{p}{q}}\newlineSo, b65×b75=b65+75b^{\frac{6}{5}} \times b^{\frac{7}{5}} = b^{\frac{6}{5} + \frac{7}{5}}
  2. Add Exponents: Add the exponents.\newline65+75=(6+7)5\frac{6}{5} + \frac{7}{5} = \frac{(6 + 7)}{5}\newline65+75=135\frac{6}{5} + \frac{7}{5} = \frac{13}{5}\newlineSo, b65b75=b135b^{\frac{6}{5}} \cdot b^{\frac{7}{5}} = b^{\frac{13}{5}}
  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, and all exponents are positive.\newlineThe final answer is b135b^{\frac{13}{5}}, which is already in the correct form.

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