4 to the power of 12, written mathematically as 412, is calculated by multiplying the number 4 by itself 12 times. This means:
412 = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
To simplify this, we can break it down step by step or use the properties of exponents. The first step is to calculate smaller powers of 4:
- 41 = 4
- 42 = 16
- 43 = 64
- 44 = 256
- 45 = 1024
Continuing this process or using a calculator will lead you to the final result. When we calculate 412, we find:
412 = 16777216
This means 4 to the power of 12 equals 16,777,216. This number is significant in various fields like computer science and mathematics, where powers of 2 and 4 are frequently encountered. Understanding how to work with exponents helps in simplifying complex problems and making calculations easier.