A biologist models a bacterial colony where each hour, the population multiplies by x. After 3 hours the multiplier is x³, and after another 4 hours it's x⁴. The combined growth factor across all 7 hours is x³ · x⁴.
Using the product of powers property, simplify x³ · x⁴ to a single power of x.
Ax⁷ — add the exponents
Bx¹² — multiply the exponents
C2x⁷ — the two factors double the coefficient
Dx¹ — subtract the exponents
Explanation
Product of powers rule: when multiplying powers with the *same base*, add the exponents → x³ · x⁴ = x^(3+4) = x⁷.
Why the distractors are wrong: (B) Multiplying exponents (3×4=12) is the power-of-a-power rule, used only for (x³)⁴ — a single power raised to another power. (C) There's only one base, x, and no separate coefficients to double. (D) Subtracting exponents is the quotient rule (x³ ÷ x⁴), used for division, not multiplication.