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

To understand why $5^0 = 1$, let’s explore the rules of exponents. When you raise a number to a power, you are essentially multiplying that number by itself a specified number of times. For instance, $5^3$ denotes $5 \times 5 \times 5$. But what occurs when the exponent is $0$?

The principle that any non-zero number raised to the power of $0$ equals $1$ is derived from the properties of exponents. One way to comprehend this is through the division rule for exponents, which states that

If we set $m = n$, we arrive at

Since any non-zero number divided by itself equals $1$, we conclude that $a^0 = 1$.

Another approach to understand this concept is to observe patterns in the powers of $5$. Consider the following sequence of powers:

Notice that each time we decrease the exponent by $1$, we divide by $5$. Thus, we can see that

This rule is applicable to any non-zero number, not just $5$. Therefore, whether we consider $2^0$, $10^0$, or even $(-3)^0$, the result will always be $1$. This fundamental property of exponents is essential for simplifying numerous mathematical expressions.