1. Problem statement: Evaluate $2 \times 10 \times 10 \times 10_2 \times 10$.\n2. Interpret the notation $10_2$ as a binary number.\nIn base 2, $10_2$ equals $1\cdot 2^1 + 0\cdot 2^0 = 2$.\n3. Replace $10_2$ by its decimal value $2$ and simplify the product.\nWe compute $2 \times 10 \times 10 \times 2 \times 10$.\nGroup as $(2 \times 2) \times (10 \times 10 \times 10)$.\nCompute $2 \times 2 = 4$ and $10 \times 10 \times 10 = 1000$.\nMultiply to obtain $4 \times 1000 = 4000$.\n4. Final answer: $4000$.\n