When any number is raised to the power of 1, the result is simply the number itself. This is based on the fundamental properties of exponents.
For example, if we take the number 5:
- 51 = 5
Similarly, if we take the number 10:
- 101 = 10
As you can see, it doesn’t matter what the base number is; as long as it’s being raised to the power of 1, the output will always be the base number itself.
This property holds true for positive numbers, negative numbers, fractions, and even zero:
- (-3)1 = -3
- (1/2)1 = 1/2
- (0)1 = 0
This simplicity makes it easy to understand why this is the case. Raising any number to the power of 1 essentially signifies that you have one of that number—no multiplication or complex operations involved. In mathematical terms, it reinforces that the identity of the number remains unchanged when exponentiated to 1.
Overall, this concept is foundational in mathematics and is a building block for understanding more complex operations involving exponents and powers.