2. \( \frac{a^{2 x} \times a^{x} b^{-2}}{a^{3 x}} \)

To simplify the expression \( \frac{a^{2 x} \times a^{x} b^{-2}}{a^{3 x}} \), we start by combining the terms in the numerator. We can use the property of exponents that states \( a^m \times a^n = a^{m+n} \). Thus, we have: \[ a^{2x} \times a^{x} = a^{2x + x} = a^{3x} \] Now substituting this into the expression gives: \[ \frac{a^{3x} b^{-2}}{a^{3x}} \] Now we can cancel \( a^{3x} \) in the numerator and denominator: \[ b^{-2} \] Since \( b^{-2} = \frac{1}{b^2} \), the final simplified expression is: \[ \frac{1}{b^2} \]