Set 4: Exponential Functions (Intermediate)

Choice A is correct. Choice A is the correct answer. Rewrite with base 3. 1. Rewrite: $27= 3^3$, so $27^{2 x} = (3^3)^{2 x}$. 2. Power rule: $(a^m)^n = a^{mn}$, so $(3^3)^{2 x} = 3^{6 x}$. 3. Verify Choice B: $9^{3 x} = (3^2)^{3 x} = 3^{6 x}$ ✓ (Also equivalent!) Strategic Tip: Multiple representations can be correct—check all options. Choice C is incorrect because $3^{3 x} = (3^3)^x = 27^x \neq 27^{2 x}$. Choice D is incorrect because $81^x = (3^4)^x = 3^{4 x} \neq 3^{6 x}$.