Any non-zero number raised to the power of $0$ is always equal to $1$.

To comprehend why $4^0$ equals $1$, let’s explore the rules governing exponents. Raising a number to a power means multiplying that number by itself a specified number of times. For instance, $4^2$ represents $4 \times 4$, which equals $16$.

Now, let’s observe the pattern that emerges when we decrease the exponent by $1$ each time:

• For $4^3$:

• For $4^2$:

• For $4^1$:

Notice that each time we reduce the exponent by $1$, we divide by $4$:

• From $4^3$ to $4^2$:

• From $4^2$ to $4^1$:

Following this pattern, if we continue to reduce the exponent from $1$ to $0$:

Thus, we conclude that $4^0$ must equal $1$. This principle is universally applicable to any non-zero number, not just $4$. The reasoning is rooted in the properties of exponents, ensuring consistency in mathematical operations.