What does it mean when a number is raised to the power of 1?

When a number is raised to the power of 1, it simply means that the number remains unchanged. Mathematically, this can be expressed as:

a¹ = a

Where a is any real number. This property holds true for all numbers, whether they are integers, fractions, or decimals.

For example:

• If you take the number 5, then 5¹ = 5.
• If you take the number 10, then 10¹ = 10.
• If you take a fraction like 1/2, then (1/2)¹ = 1/2.

This property of numbers can be very helpful in simplifying expressions in algebra and calculus, as it allows us to understand exponents more intuitively. Raising a number to the power of 1 is one of the foundational rules of exponents and exemplifies the identity property of multiplication, which states that any number multiplied by one remains unchanged.

In summary, when a number is raised to the power of 1, it retains its original value, making it a straightforward yet essential concept in mathematics.