If x is a nonzero number, what is x^0?

If x is a nonzero number, what is x^0?

• A. 1
• B. x
• C. 0
• D. undefined

Answer: (A)

Raising a nonzero number to the zero power yields 1. This keeps the rules for exponents consistent. A solid way to see it is through division: for any nonzero x and any integer n, x^n / x^n = 1. But x^n / x^n also equals x^{n-n} = x^0. Since the left side is 1, the right side must be 1, so x^0 = 1. For a concrete check, think of x as 5: going from 5^1 to 5^0 would involve dividing by 5, leaving 1, which matches the idea that the zero-power form is the multiplicative identity. This rule applies as long as the base isn’t zero; 0^0 is a different, indeterminate case. So the value is 1.

Raising a nonzero number to the zero power yields 1. This keeps the rules for exponents consistent. A solid way to see it is through division: for any nonzero x and any integer n, x^n / x^n = 1. But x^n / x^n also equals x^{n-n} = x^0. Since the left side is 1, the right side must be 1, so x^0 = 1. For a concrete check, think of x as 5: going from 5^1 to 5^0 would involve dividing by 5, leaving 1, which matches the idea that the zero-power form is the multiplicative identity. This rule applies as long as the base isn’t zero; 0^0 is a different, indeterminate case. So the value is 1.