Let's calculate 25 times 32 times 125 using smart calculation methods. First, we identify that 25 and 125 are special numbers. 25 equals 5 squared, and 125 equals 5 cubed. This gives us a clue for efficient calculation.
Now we use the associative property to group 25 and 125 together. We can rewrite the expression as 25 times 125, times 32. Let's calculate 25 times 125 first. Since 25 equals 5 squared and 125 equals 5 cubed, we get 5 to the power of 5, which equals 3125.
Now we calculate 3125 times 32. We can break down 32 into 4 times 8, which makes the calculation easier. First, 3125 times 4 equals 12500. Then, 12500 times 8 equals 100000. So our final answer is 100000.
Let's review our complete solution. We started with 25 times 32 times 125. By grouping 25 and 125 together, we got 3125 times 32. Then we broke down 32 into 4 times 8, calculated step by step, and arrived at our final answer of 100000. The key insight was to group numbers with compatible factors, making the calculation much simpler than doing it directly.