Question

Why do we subtract exponents when we are
dividing like bases?

Answer 1

When we divide like bases with exponents, we subtract the exponents because we are essentially canceling out the common factors of the bases.

For example, when dividing x^5 by x^3, we are essentially dividing x * x * x * x * x by x * x * x. This leaves us with x^2, as we have cancelled out three x's, which corresponds to subtracting the exponents (5 - 3 = 2).

In general, when we divide like bases with exponents, we subtract the exponents to simplify the expression by canceling out the common factors of the bases.