Answer: C

Write $4^x$ as $(2^2)^x = 2^{2x}$. Then $4^x \cdot 2^{x + 3} = 2^{2x} \cdot 2^{x + 3} = 2^{3x + 3}$. Since $3x + 3 = 3(x + 1)$, this equals $(2^3)^{x + 1} = 8^{x + 1}$.

Choice D correctly combines $4^x \cdot 2^x$ into $8^x$, but the leftover factor $2^3 = 8$ adds only $1$ to the exponent of $8$, not $3$.

Why the other choices are wrong

• A. This adds the bases 4 and 2. Exponent rules need a common base, and bases are never added.
• B. This multiplies the bases and adds the exponents. Exponents add only when the bases are the same.
• D. Combining 4 to the x and 2 to the x into 8 to the x is right, but the extra factor 2³ = 8 adds only 1 to the exponent of 8.