Potensregler

Potensregler, also known as exponent rules, are a set of mathematical principles that govern how exponents are manipulated in algebraic expressions. These rules provide a standardized way to simplify and combine terms involving powers.

One fundamental rule states that when multiplying powers with the same base, you add their exponents. For example, x^a * x^b = x^(a+b). Conversely, when dividing powers with the same base, you subtract the exponent of the denominator from the exponent of the numerator: x^a / x^b = x^(a-b).

Another key rule deals with raising a power to another power. In this case, you multiply the exponents: (x^a)^b = x^(a*b). When a product or quotient is raised to a power, the exponent applies to each factor within the parentheses: (xy)^a = x^a * y^a and (x/y)^a = x^a / y^a.

The exponent of zero is always one for any non-zero base, meaning x^0 = 1. A negative exponent indicates a reciprocal; x^-a is equivalent to 1/x^a. These rules are essential for simplifying complex expressions and are foundational in algebra, calculus, and many other areas of mathematics. Understanding and applying these rules efficiently is crucial for mathematical proficiency.