A common question I hear from students is: why does a number raised to the power of 0 equal 1? The explanation can be found by observing patterns in the data. A number raised to a power is the number multiplied by itself as many times as the power. For example, 2 to the power of 3 is equal to 2×2×2 = 8. Two to the power of 2 is 2×2 = 4. Note that going from 2 to the power of 3 to 2 to the power of 2 involves a division by 2. This pattern continues for 2 to the power of 1.

If we continue with this pattern, we determine that 2 to the power of 0 is 1. We can extend this process to negative powers such as 2 to the power of -1, -2 and so on.

In some cases, mathematical concepts can be explained by identifying patterns like this.

What other mathematical questions do you have?