When we multiply something by 10, we move the decimal point one space to the right. When we multiply something by 0.1, we move the decimal point one space to the left. When we multiply something by 0.01, we move the decimal point two spaces to the left. Following this pattern, when we multiply something by 0.001, we move the decimal point three spaces to the left. This is why we can write 0.001 as \(10^{-3}\).

So, multiplying 0.001 by itself will add three more 0s. Hence, 0.001 × 0.001 = 0.000001. Multiplying once more will add another three 0s, so \((0.001)^{3}\) = 0.000000001. You can see that to get from there to 0.1, we have to move the decimal point to the right 8 times. So 0.1 is 8 times greater than 0.000000001.