Exponentiation

Exponentiation is a mathematical operation that represents repeated multiplication of the same number. In an exponentiation expression, the number being multiplied is called the base, and the number of times it is multiplied by itself is called the exponent.

The general form of an exponentiation expression is:

base^exponent

For example, in the expression 2³, the base is 2 and the exponent is 3. This represents 2 multiplied by itself 3 times, which equals 8.

Exponentiation can be performed with both whole numbers and fractions. When raising a number to a negative exponent, it represents the reciprocal of the number raised to the positive exponent.

Exponentiation is a fundamental operation in mathematics and is used in many different areas, including algebra, calculus, and physics.

Here are a few examples of exponentiation:

1. 2⁴ = 2 * 2 * 2 * 2 = 16
2. 5² = 5 * 5 = 25
3. (1/2)³ = (1/2) * (1/2) * (1/2) = 1/8
4. 3^-2 = 1 / (3²) = 1/9

Exponentiation is a powerful mathematical concept that allows for the efficient representation of repeated multiplication, making it an important tool in problem-solving and mathematical modeling.