Indekssummasjonsregler

Indekssummasjonsregler, also known as index laws or exponent rules, are a set of mathematical principles used to simplify expressions involving exponents. These rules apply to both positive and negative exponents, as well as to fractional and irrational exponents. The primary index laws include:

1. Product of Powers: When multiplying two expressions with the same base, you can add the exponents. For example, a^m * a^n = a^(m+n).

2. Quotient of Powers: When dividing two expressions with the same base, you can subtract the exponents. For example, a^m / a^n = a^(m-n).

3. Power of a Power: When raising an expression to a power, you can multiply the exponents. For example, (a^m)^n = a^(m*n).

4. Zero Exponent: Any non-zero number raised to the power of zero is equal to 1. For example, a^0 = 1.

5. Negative Exponent: A negative exponent indicates that the base is in the denominator. For example, a^-n = 1/a^n.

6. Fractional Exponent: A fractional exponent indicates that the base is the radicand and the denominator of the exponent is the index of the root. For example, a^(1/n) = n√a.

These rules are fundamental in algebra and calculus, allowing for the simplification of complex expressions and the solution of various mathematical problems. They are widely used in fields such as physics, engineering, and computer science.