To find the value of 7 raised to the power of 4, we perform the following calculation:
- 7 to the power of 1 is 7.
- 7 to the power of 2 is 7 x 7 = 49.
- 7 to the power of 3 is 7 x 7 x 7 = 343.
- 7 to the power of 4 is 7 x 7 x 7 x 7.
Now calculating this step-by-step, we can simplify it:
- First, calculate 7 x 7 = 49.
- Then take that result and multiply by 7 again: 49 x 7 = 343.
- Finally, multiply 343 by 7: 343 x 7 = 2401.
Therefore, 7 raised to the power of 4 is 2401. This exponential notation shows how many times to multiply the number 7 by itself, which gives us a significant value in mathematics.
Understanding exponentiation is fundamental in various fields, including science, engineering, and finance, as it helps in modeling growth, calculating interest, and much more.