exponentiëring

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 4 times, which is 3 * 3 * 3 * 3 = 81. The base is the number being multiplied, and the exponent indicates how many times the base is used as a factor.

When the exponent is a positive integer, exponentiation is straightforward repeated multiplication. For instance, 5^3 = 5 * 5 * 5 = 125. If the exponent is 1, the result is simply the base itself (e.g., 7^1 = 7). An exponent of 0 typically results in 1 for any non-zero base (e.g., 2^0 = 1).

Negative exponents indicate reciprocals. For example, b^-n is equal to 1 / (b^n). So, 2^-3 = 1 / (2^3) = 1 / 8. Fractional exponents represent roots. For instance, b^(1/n) is the nth root of b. Thus, 9^(1/2) is the square root of 9, which is 3.

Exponentiation is a fundamental concept in algebra and is used extensively in various fields, including science, engineering, finance, and computer science. It allows for concise representation of very large or very small numbers and simplifies complex calculations involving repeated multiplication.