Why do we subtract exponents when we are dividing like bases?
When we divide like bases, we subtract exponents because it is a simplified way of expressing repeated multiplication.
To understand why we subtract exponents, let's consider an example:
If we have x^5 divided by x^2, we can rewrite this as (x * x * x * x * x) divided by (x * x).
When we divide, we are essentially canceling out common factors, which in this case are two x's. We can divide two x's from the numerator and denominator and are left with (x * x * x), which is equal to x^3.
This process of dividing the common factors is equivalent to subtracting the exponents. In this case, 5 - 2 = 3.
So, when we divide like bases, we subtract the exponents because we are essentially canceling out common factors by subtracting the number of times the base appears in the denominator from the number of times it appears in the numerator.