The Exponent of One Rule states that any number or variable raised to the power of one is equal to itself. Mathematically, this is written as:

$$a^1 = a$$

for any real number or variable ( a ).

Explanation

• When you raise a number to the power of one, you are essentially multiplying it by itself only once, which does not change its value.
• This rule applies to all numbers, including fractions, decimals, and even variables.

Examples

1. ( 5^1 = 5 )
2. ( (-3)^1 = -3 )
3. ( x^1 = x ) (for any variable ( x ))
4. ( \left( \frac{7}{2} \right)^1 = \frac{7}{2} )

This rule is useful in algebraic simplifications and exponent operations.

Latex

a^1 = a