Although the terms exponent and power are often used in a similar way, they do not mean exactly the same thing. The exponent tells us how many times a number is multiplied by itself, while the power represents the complete expression formed by the base and the exponent or its final value.
This table compares exponent and power according to several criteria:
Characteristic | Exponent | Power |
|---|---|---|
Definition | The multiplicity of a base by itself is represented by this number. | a base raised to an exponent's result. |
Notation | Appears as a superscript to the right of the base (e.g., in 23, 3 is the exponent). | Refers to the entire expression (e.g., in 23 = 8, 8 is the power). |
Role | shows how often the base is applied as a factor. | describes the operation's result. |
Components | A portion of the statement designates the base operation to be carried out. | the value that results from carrying out the operation that the exponent indicates. |
Example | In 72 = 49, 2 is the exponent. | In 72 = 49, 49 is the power. |
Context of Use | used to define the calculation process required to determine the power. | used to express how exponentiation produces a numerical result. |
Formula Representation | The portion of the base-exponent notation that shows how frequently the base is a factor. | the whole expression, which yields a particular value and includes the base and the exponent. |
Examples on Exponent and Power
Example 1: What is the value of 24?
= 24
= 2 × 2 × 2 × 2 = 16
Example 2: What is 30?
30 = 1
Example 3: Simplify: (23)2.
(23)2 = 23×2
= 26= 2 × 2 × 2 × 2 × 2 × 2
= 64
Example 4: What is 3.2×103 in standard form?
3.2 × 103 = 3200
Example 5: What is the value of (-2)4?
(-2)4 = -2 × -2 × -2 × -2
= 16
Practice Questions on Exponent and Power
Q1. Simplify 52 × 53
Q2. What is 70?
Q3. Simplify: 54 / 53.
Q4. What is 3-2.
Q5. What is ( 2 × 5)3.
Answer Key
- Answer 1: 55
- Answer 2: 1
- Answer 3: 5
- Answer 4: 1/9
- Answer 4: 1000
Also Check
- Properties of Exponents
- Real-Life Applications of Exponent and Power