In mathematics, any non-zero number raised to the power of zero is defined to be 1. This includes negative numbers as well. So, when we raise a negative number, such as -5, to the power of 0, the result is:
-50 = 1
This rule stems from the properties of exponents. To understand why this is the case, consider the law of exponents that states:
- am ÷ an = am-n
Using this law, if we take a negative number, say -5, and divide it by itself, we get:
-51 ÷ -51 = -51-1 = -50
Now, since any non-zero number divided by itself equals 1, we can conclude that:
-50 = 1
It’s important to note that the only exception to this rule is when the base is zero. The expression 00 is considered indeterminate in many contexts. However, for all other negative and positive numbers, raising them to the power of zero gives us 1. This principle is fundamental in mathematics and is widely accepted in various branches of science and engineering as well.