exponentación

Exponentiation is a mathematical operation, written as b^n, involving two numbers, the base b and the exponent (or power) n. It is the result of repeatedly multiplying the base by itself n times. For example, 3^4 means 3 multiplied by itself four times, which is 3 × 3 × 3 × 3 = 81.

The exponent indicates how many times the base is used as a factor. In the expression b^n, b is the base and n is the exponent. If n is a positive integer, b^n is simply b multiplied by itself n times. If n is zero, b^0 is defined as 1 for any non-zero base b. If n is a negative integer, b^n is equal to 1 divided by b raised to the positive exponent -n, i.e., b^-n = 1/b^n.

Exponentiation is fundamental in many areas of mathematics and science. It is used in polynomial expressions, scientific notation, compound interest calculations, and the study of growth and decay phenomena. Fractional exponents, such as b^(1/m), represent roots, where b^(1/m) is the m-th root of b. For instance, 9^(1/2) is the square root of 9, which is 3. The general form of fractional exponents, b^(m/n), combines both root and power operations.