Exponentiace

Exponentiation is a mathematical operation, written as b^n, involving two numbers, the base b and the exponent or power n. It is defined as the result of multiplying the base by itself n times. For example, 2^3 means 2 multiplied by itself 3 times, which is 2 * 2 * 2 = 8. The number 8 is the result or power.

If the exponent n is a positive integer, exponentiation is simply repeated multiplication. If n is 0, b^0 is defined as 1 for any non-zero base b. If the exponent is a negative integer, say -n, then b^-n is equal to 1 divided by b^n, provided b is not zero. For example, 2^-3 is 1/2^3, which equals 1/8.

Fractional exponents represent roots. For instance, b^(1/m) is the m-th root of b. The expression b^(n/m) is equivalent to (b^n)^(1/m) or (b^(1/m))^n. Exponentiation is a fundamental operation in many areas of mathematics, science, and engineering, appearing in formulas for growth, decay, and compound interest, among other applications. It's also a key concept in algebra and calculus.