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Simplify. Assume all variables are positive.\newlineb115b125b^{\frac{11}{5}} \cdot b^{\frac{12}{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.\newlineb115b125b^{\frac{11}{5}} \cdot b^{\frac{12}{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 Property: Identify the equation and apply the property of exponents for multiplying with the same base: bm×bn=b(m+n)b^m \times b^n = b^{(m+n)}.
  2. Apply Exponent Rule: We have: b115b125b^{\frac{11}{5}} \cdot b^{\frac{12}{5}}. Add the exponents since the bases are the same.\newlineb115+125=b235b^{\frac{11}{5} + \frac{12}{5}} = b^{\frac{23}{5}}.
  3. Final Simplification: The expression b235b^{\frac{23}{5}} is already simplified and has a positive exponent. There is no need to simplify further.

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