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Simplify. Assume all variables are positive.\newlineu74u74u^{\frac{7}{4}} \cdot u^{\frac{7}{4}}\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.\newlineu74u74u^{\frac{7}{4}} \cdot u^{\frac{7}{4}}\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: 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}.\newlineSo, u74×u74=u74+74u^{\frac{7}{4}} \times u^{\frac{7}{4}} = u^{\frac{7}{4} + \frac{7}{4}}.
  2. Add Exponents: Add the exponents. 74+74=144.\frac{7}{4} + \frac{7}{4} = \frac{14}{4}.
  3. Simplify Fraction: Simplify the fraction 14/414/4. 14/414/4 can be simplified to 3.53.5 or, more appropriately for exponents, 7/27/2.
  4. Write Final Answer: Write the final answer using the simplified exponent. u74×u74=u72u^{\frac{7}{4}} \times u^{\frac{7}{4}} = u^{\frac{7}{2}}.

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