What is the value of the expression 1^n?

What is the value of the expression 1^n?

• A. 0
• B. 1
• C. -1
• D. n

Answer: (B)

The expression \(1^n\) represents 1 raised to the power of \(n\), where \(n\) can be any real number. No matter what the value of \(n\) is, as long as \(n\) is a finite number, the result will always be 1. This is due to the property of exponents which states that any non-zero number raised to the power of zero is 1, and additionally, any number raised to any power will yield a consistent outcome when that number is 1. Therefore, \(1^n\) results in 1 because multiplying 1 by itself \(n\) times still results in 1. This property applies regardless of whether \(n\) is a positive integer, a negative number, or zero. It’s a fundamental rule in mathematics that makes evaluating powers of 1 straightforward and consistent. Hence, the correct answer is indeed 1.

The expression (1^n) represents 1 raised to the power of (n), where (n) can be any real number. No matter what the value of (n) is, as long as (n) is a finite number, the result will always be 1. This is due to the property of exponents which states that any non-zero number raised to the power of zero is 1, and additionally, any number raised to any power will yield a consistent outcome when that number is 1.

Therefore, (1^n) results in 1 because multiplying 1 by itself (n) times still results in 1. This property applies regardless of whether (n) is a positive integer, a negative number, or zero. It’s a fundamental rule in mathematics that makes evaluating powers of 1 straightforward and consistent. Hence, the correct answer is indeed 1.