4 to the power of 0 is equal to 1. This may seem a bit puzzling at first, but it actually follows a simple mathematical rule regarding exponents.
The rule states that any non-zero number raised to the power of 0 is always equal to 1. So whether it’s 4, 10, or even a fraction like 1/2, the result will remain 1. This is largely to maintain the consistency of the laws of exponents.
To understand why this is true, consider the pattern of powers of 4:
- 43 = 64
- 42 = 16
- 41 = 4
- 40 = ?
If we follow the pattern of dividing by 4, we see:
- 43 (64) divided by 4 = 42 (16)
- 42 (16) divided by 4 = 41 (4)
- 41 (4) divided by 4 = 40 (1)
This division leads us to conclude that 40 must be 1, so that the pattern holds true. Thus, the final answer is that 4 to the power of 0 equals 1.