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Simplify. Assume all variables are positive.\newlinew43w43w^{\frac{4}{3}} \cdot w^{\frac{4}{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.\newlinew43w43w^{\frac{4}{3}} \cdot w^{\frac{4}{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 and apply exponent rule: Identify the equation and apply the exponent multiplication rule.\newlineWhen multiplying two exponents with the same base, we add the exponents: am×an=am+na^m \times a^n = a^{m+n}.\newlinew43×w43=w43+43w^{\frac{4}{3}} \times w^{\frac{4}{3}} = w^{\frac{4}{3} + \frac{4}{3}}.
  2. Add exponents: Add the exponents.\newline43+43=83\frac{4}{3} + \frac{4}{3} = \frac{8}{3}.\newlineSo, w43×w43=w83w^{\frac{4}{3}} \times w^{\frac{4}{3}} = w^{\frac{8}{3}}.
  3. Write final answer: Write the final answer.\newlineThe simplified form of w43×w43w^{\frac{4}{3}} \times w^{\frac{4}{3}} is w83w^{\frac{8}{3}}.

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