Set 11: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Use quotient rule for exponentials. 1. Rule: $\frac{a^m}{a^n} = a^{m-n}$. 2. Apply: $\frac{e^{5 x}}{e^{2 x}} = e^{5 x-2 x} = e^{3 x}$. Strategic Tip: When dividing same bases, subtract exponents. Choice B is incorrect because this adds exponents (multiplication rule). Choice C is incorrect because this multiplies exponents. Choice D is incorrect because $x$ should remain in the exponent.