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Simplify. Assume all variables are positive.\newlinex94×x94x^{\frac{9}{4}} \times x^{\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.\newlinex94×x94x^{\frac{9}{4}} \times x^{\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: Identify the equation and apply the property of exponents for multiplication, which states that when you multiply like bases, you add the exponents: xa×xb=x(a+b)x^a \times x^b = x^{(a+b)}.
  2. Calculate Exponents: Calculate the sum of the exponents: (94)+(94)(\frac{9}{4}) + (\frac{9}{4}).
  3. Perform Addition: Perform the addition: (94)+(94)=184(\frac{9}{4}) + (\frac{9}{4}) = \frac{18}{4}.
  4. Simplify Exponent: Simplify the exponent: 184\frac{18}{4} can be reduced to 92\frac{9}{2}, since both numerator and denominator are divisible by 22.
  5. Write Final Answer: Write the final answer using the simplified exponent: x92x^{\frac{9}{2}}.

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