Part 3/6:
When dividing powers with the same base, you can subtract their exponents. Thus, ( \frac{x^a}{x^b} = x^{a-b} ). For instance, in ( \frac{x^3}{x^2} ), you would have ( x^{3-2} = x^1 ).
This simplification demonstrates the elegance of exponent rules, leading to a more intuitive understanding of how powers function.
Negative Exponents
In the context of negative exponents, the rule becomes even clearer: ( x^{-a} = \frac{1}{x^a} ). For example, ( x^{-2} ) is the same as ( \frac{1}{x^2} ). This property reinforces the idea that negative powers simply represent the reciprocal of the base raised to the positive exponent.