In mathematics, the terms "exponent" and "power" are closely related but distinct concepts describing how a number is repeatedly multiplied by itself. The key difference lies in what each term represents within the expression.
Understanding Exponents
The exponent, also known as the index or power, is the small, raised number written to the upper right of a base number. It indicates how many times the base number is multiplied by itself.
- For example, in the expression 5³, the exponent is 3. This means 5 is multiplied by itself three times: 5 x 5 x 5 = 125.
Understanding Power
The power refers to the entire expression – the base number raised to the exponent. It represents the result of the repeated multiplication.
- In the expression 5³, the power is 125 (the result of 5 x 5 x 5).
In essence: The exponent tells you what to do, while the power is what you get after performing the operation.
Examples
| Expression | Base | Exponent | Power | Calculation |
|---|---|---|---|---|
| 2⁴ | 2 | 4 | 16 | 2 x 2 x 2 x 2 = 16 |
| 10² | 10 | 2 | 100 | 10 x 10 = 100 |
| 3¹ | 3 | 1 | 3 | 3 = 3 |
| xⁿ | x | n | xⁿ | x multiplied by itself n times |
The provided references consistently support this distinction: the exponent specifies the number of times the base is multiplied, while the power is the final numerical result of this repeated multiplication. One source clarifies that the power is a way of describing what the exponent is doing to the base.
