Final answer:
To simplify 4d^-6 times 3d^-6, multiply the coefficients (4 and 3) to get 12, and add the exponents of 'd' (-6 and -6) to get -12, resulting in the simplified expression 12d^-12.
Step-by-step explanation:
To simplify 4d^-6 times 3d^-6 using the product rule, we first recognize that both terms involve 'd' raised to a negative exponent. The product rule for exponents tells us that when we multiply two exponential expressions with the same base, we add their exponents.
The expression can be rewritten as:
(4 × 3) × d^(-6 + -6)
Multiplying the coefficients separately from the variables with exponents:
12 × d^(-12)
Therefore, the simplified form of the expression is 12d^-12.