Exponenter

Exponenter, also known as exponents or powers, are mathematical expressions that denote repeated multiplication of a number by itself. An exponent consists of a base and an exponent (or power), written as base^exponent, where the exponent indicates how many times the base is multiplied by itself. For example, 3^4 equals 3 multiplied by itself four times: 3 × 3 × 3 × 3, which equals 81.

Exponents are fundamental in various branches of mathematics, including algebra, calculus, and scientific notation. They simplify the expression of very large or very small numbers. Exponent rules include properties like the product rule, which states that a^m × a^n = a^(m + n); the quotient rule, a^m ÷ a^n = a^(m - n); and the power of a power rule, (a^m)^n = a^(m × n).

Exponents can be positive, negative, or fractional. Negative exponents represent reciprocals; for example, a^(-n) equals 1 / a^n, provided a ≠ 0. Fractional exponents describe roots, where a^(1/n) represents the n-th root of a. For instance, 8^(1/3) equals the cube root of 8, which is 2.

Exponents are essential in expressing exponential growth or decay, such as population increase, radioactive decay, and compound interest calculations. They also underpin many mathematical concepts and theories, making them a key element in both theoretical and applied mathematics.