Unraveling the Mystery of 0^0: Is It Indeterminate?

To solve the problem of evaluating $0^0$, we need to analyze the properties of exponents and related mathematical principles:

• Typically, for any number $b$, the expression $b^0 = 1$. However, $b^0$ assumes $b \neq 0$. When $b$ is zero, this rule conflicts with the intuitive case that would suggest $0^n = 0$ for any positive integer $n$.

• In mathematics, $0^0$ arises in contexts where it could be considered both zero and one depending on the operation taken to the limit in functions. For example, evaluating limits involving forms like $(x^x)$ as $x \to 0$ can show indeterminacy.

• Thus, $0^0$ is not defined within the normal arithmetic rules we apply to exponents because it does not yield a consistent value across mathematical contexts. Historically, it is generally considered indeterminate.

Therefore, $0^0$ is not defined.