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Simplify. Assume all variables are positive.\newlineb13b23b^{\frac{1}{3}} \cdot b^{\frac{2}{3}}\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.\newlineb13b23b^{\frac{1}{3}} \cdot b^{\frac{2}{3}}\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 powers with the same base, we add the exponents.\newlineb13×b23=b13+23b^{\frac{1}{3}} \times b^{\frac{2}{3}} = b^{\frac{1}{3} + \frac{2}{3}}
  2. Add Exponents: Add the exponents.\newline13+23=33\frac{1}{3} + \frac{2}{3} = \frac{3}{3}
  3. Simplify Exponents: Simplify the sum of the exponents. 33=1\frac{3}{3} = 1
  4. Apply Exponent to Base: Apply the simplified exponent to the base bb.b33=b1b^{\frac{3}{3}} = b^1
  5. Simplify Expression: Simplify the expression b1b^1. b1b^1 is simply bb, since any number raised to the power of 11 is itself.

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