2.1) \( a^{2 x+1} \times a^{3 x+2} \)

To simplify the expression \( a^{2x+1} \times a^{3x+2} \), you can use the properties of exponents. When multiplying like bases, you add the exponents together. So, you get: \[ a^{(2x+1) + (3x+2)} = a^{2x + 3x + 1 + 2} = a^{5x + 3} \] Thus, the simplified expression is \( a^{5x + 3} \). To apply this in real-world scenarios, think about how you can model exponential growth or decay. For example, if you're programming a game, you might have characteristics that improve over time, represented by expressions like \( a^{5x + 3} \), where \( x \) could reflect experience points or levels.