Eksponendid

Eksponendid is a term used in mathematics to describe a number raised to a power. It is commonly written as a^b, where 'a' is the base and 'b' is the exponent. The exponent indicates how many times the base is multiplied by itself. For example, 2^3 means 2 multiplied by itself three times, which is 2 * 2 * 2 = 8.

The exponent can be a positive integer, a negative integer, a fraction, or even an irrational number. When the exponent is 0, the result is always 1, provided the base is not 0. A negative exponent, such as a^-b, is equivalent to 1 divided by the base raised to the positive exponent (1/a^b). Fractional exponents, like a^(1/n), represent roots, where a^(1/n) is the nth root of 'a'.

Properties of exponents simplify calculations. For instance, when multiplying numbers with the same base, the exponents are added: a^m * a^n = a^(m+n). When dividing numbers with the same base, the exponents are subtracted: a^m / a^n = a^(m-n). Raising a power to another power involves multiplying the exponents: (a^m)^n = a^(m*n). These rules are fundamental to algebraic manipulations and understanding various mathematical concepts.