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

Answer 1

When dividing like bases with exponents, we subtract the exponents because it represents the ratio of the two quantities. For example, if we have x^a / x^b, we can rewrite this as x^(a-b). This is because when we divide two like bases with exponents, we are essentially canceling out the common factors between the two bases, leaving us with the difference of the exponents. This rule follows the general rule of exponents, which states that when we divide two like bases with exponents, we subtract the exponents.