Question

Evaluate the expression. \(0^{-4}\)

Short answer

The expression \(0^{-4}\) is undefined.

Step-by-step solution

Understanding Negative Exponents

Normally, a negative exponent means we take the reciprocal of the base. For example, \(2^{-3}\) would be equal to \(\frac{1}{2^3}\). However, there is an exception for zero. When 0 is raised to a negative power, we cannot take the reciprocal because we cannot divide by zero.

Evaluating the Expression

In this exercise, evaluating \(0^{-4}\) will result in an undefined value, because the concept of negative exponents assumes taking the reciprocal of the base, and we can't divide by zero.