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Simplify. Assume all variables are positive.\newlinew54w94w^{\frac{5}{4}} \cdot w^{\frac{9}{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.\newlinew54w94w^{\frac{5}{4}} \cdot w^{\frac{9}{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 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}.\newlinew54×w94=w54+94w^{\frac{5}{4}} \times w^{\frac{9}{4}} = w^{\frac{5}{4} + \frac{9}{4}}.
  2. Add Exponents: Add the exponents. 54+94=144.\frac{5}{4} + \frac{9}{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. w54×w94=w72w^{\frac{5}{4}} \times w^{\frac{9}{4}} = w^{\frac{7}{2}}.

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