Zero Power Rule using division of like bases:
The zero power rule states that any non-zero number raised to the power of zero is equal to 1.
Now, let's consider the division of like bases. When dividing two numbers with the same base, we subtract their exponents.
For example, if we have (a^m)/(a^n), where a is a non-zero number, and m and n are any real numbers, we can write it as:
(a^m)/(a^n) = a^(m-n)
Using the zero power rule, if we have (a^0)/(a^n), we can rewrite it as:
(a^0)/(a^n) = a^(0-n)
Since any number minus itself is equal to zero, we have:
(a^0)/(a^n) = a^0 = 1
Therefore, when dividing like bases, if the exponent of the numerator is zero, the result is always equal to 1.