A number produced by raising a base to an exponent is called a power.
Understanding Powers
A power represents repeated multiplication of a base number by itself, as many times as indicated by the exponent. According to the reference, a power "is a number produced by raising a base to an exponent." Let's break this down:
- Base: The number being multiplied.
- Exponent: The number of times the base is multiplied by itself.
- Power: The result of the exponentiation.
For example, in the expression 23:
- 2 is the base.
- 3 is the exponent.
- 23 = 2 2 2 = 8, so 8 is the power.
Examples of Powers
Here are some examples to further illustrate the concept:
| Base | Exponent | Power (Calculation) | Result |
|---|---|---|---|
| 3 | 2 | 3 * 3 | 9 |
| 5 | 3 | 5 5 5 | 125 |
| 10 | 4 | 10 10 10 * 10 | 10,000 |
| 2 | 0 | 1 (Any number to the power of 0 equals 1) | |
| 4 | -1 | 1 / 4 | 0.25 (Negative exponent indicates reciprocal) |
Real-World Applications
Powers are fundamental in many areas of mathematics, science, and engineering. They appear in:
- Scientific notation: Expressing very large or very small numbers concisely (e.g., 6.022 x 1023).
- Compound interest: Calculating the future value of an investment.
- Computer science: Representing data sizes (e.g., kilobytes, megabytes, gigabytes).
- Geometry: Calculating areas and volumes.
- Physics: Describing exponential decay or growth.
