If x is a non-zero number, what is the value of x^0?

If x is a non-zero number, what is the value of x^0?

• A. 0
• B. x
• C. 1
• D. Undefined

Answer: (C)

The value of \( x^0 \) for any non-zero number \( x \) is defined as 1. This is based on the properties of exponents. According to these properties, for any non-zero base \( x \), when you raise it to the power of zero, the result is always 1. This can be understood through the notion of division of powers. For example, if you take \( x^n \) and divide it by \( x^n \) (where \( n \) is a positive integer), the result simplifies to: \[ \frac{x^n}{x^n} = x^{n-n} = x^0 \] Since \( \frac{x^n}{x^n} \) equals 1 (as long as \( x \) is not zero), it follows that \( x^0 \) must equal 1. Thus, when \( x \) is any non-zero number, raising it to the power of zero yields a consistent and well-established result: 1. This rule is foundational in algebra and is applicable to all non-zero bases.

The value of ( x^0 ) for any non-zero number ( x ) is defined as 1. This is based on the properties of exponents. According to these properties, for any non-zero base ( x ), when you raise it to the power of zero, the result is always 1.

This can be understood through the notion of division of powers. For example, if you take ( x^n ) and divide it by ( x^n ) (where ( n ) is a positive integer), the result simplifies to:

[

\frac{x^n}{x^n} = x^{n-n} = x^0

]

Since ( \frac{x^n}{x^n} ) equals 1 (as long as ( x ) is not zero), it follows that ( x^0 ) must equal 1.

Thus, when ( x ) is any non-zero number, raising it to the power of zero yields a consistent and well-established result: 1. This rule is foundational in algebra and is applicable to all non-zero bases.