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Simplify. Assume all variables are positive.\newlineu85u125u^{\frac{8}{5}} \cdot u^{\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.\newlineu85u125u^{\frac{8}{5}} \cdot u^{\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 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: am×an=am+na^m \times a^n = a^{m+n}.\newlineu85×u125=u85+125u^{\frac{8}{5}} \times u^{\frac{12}{5}} = u^{\frac{8}{5} + \frac{12}{5}}.
  2. Add Exponents: Add the exponents.\newline85+125=(8+12)5=205\frac{8}{5} + \frac{12}{5} = \frac{(8 + 12)}{5} = \frac{20}{5}.
  3. Simplify Fraction: Simplify the fraction 20/520/5. \newline20/5=420/5 = 4.
  4. Write Final Answer: Write the final answer using the simplified exponent. u205=u4u^{\frac{20}{5}} = u^4.

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