Why do we subtract exponents when we are dividing like bases
When we divide numbers or variables with like bases, we subtract the exponents because it is the same as multiplying them by the reciprocal or inverse of the divisor.
To understand this, let's consider an example: 8^4 / 8^2
The base here is 8, and we have two exponents: 4 and 2. When we divide these two terms, we can express it as 8^4 * 1/8^2.
Using the property of multiplying exponents with the same base, we add the exponents: 8^(4+(-2)), which simplifies to 8^2. So, 8^4 / 8^2 equals 8^2.
In general, when we divide numbers with like bases, we subtract the exponents because multiplying by the reciprocal is equivalent to dividing.