Set 7: Exponential Functions (Advanced)

Choice A is correct. Choice A is the correct answer. Rewrite the base as a power of 2. 1. Rewrite base: $16= 2^4$. 2. Substitute: $16^x = (2^4)^x$. 3. Power rule: $(a^m)^n = a^{mn}$, so $(2^4)^x = 2^{4 x}$. 4. Verify Choice C: $4^{2 x} = (2^2)^{2 x} = 2^{4 x}$ ✓ (Also correct!) Strategic Tip: Both A and C are mathematically equivalent to $16^x$. Choice B is incorrect because $2^{x+4} = 2^x \cdot 2^4 = 16 \cdot 2^x \neq 16^x$. Choice D is incorrect because $2^x \cdot 8^x = 2^x \cdot 2^{3 x} = 2^{4 x}$, which equals $16^x$ (valid alternative).