1. The problem is to solve the product of two numbers: $0.004 \times 0.0004$. 2. Convert the decimals to scientific notation for easier multiplication: $$0.004 = 4 \times 10^{-3}$$ $$0.0004 = 4 \times 10^{-4}$$ 3. Multiply the numbers and the powers of ten separately: $$4 \times 4 = 16$$ $$10^{-3} \times 10^{-4} = 10^{-7}$$ 4. Combine the results: $$16 \times 10^{-7}$$ 5. Express the answer in standard decimal form: $$16 \times 10^{-7} = 1.6 \times 10^{-6} = 0.0000016$$ Final answer: $0.0000016$