To calculate 2 to the power of 15, we are essentially multiplying the number 2 by itself 15 times. In mathematical terms, this can also be expressed as:
- 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
Alternatively, using the exponentiation formula:
215
When we perform this multiplication, we find:
- 21 = 2
- 22 = 4
- 23 = 8
- 24 = 16
- 25 = 32
- 26 = 64
- 27 = 128
- 28 = 256
- 29 = 512
- 210 = 1024
- 211 = 2048
- 212 = 4096
- 213 = 8192
- 214 = 16384
- 215 = 32768
Therefore, the result of 2 to the power of 15 is 32768.
This concept of exponentiation is quite significant in mathematics and various applications, especially in computer science where powers of two often come into play, such as in binary systems and data structures.