Understanding Exponents
An exponent refers to the number of times a number (the base) is multiplied by itself. It's a shorthand way of writing repeated multiplication. For example, 23 is the same as 2 × 2 × 2, which equals 8.
Key Concepts of Exponents
- Base: The number being multiplied. In xn, 'x' is the base.
- Exponent (or Power): The number of times the base is multiplied by itself. In xn, 'n' is the exponent.
- Positive Exponents: Indicate repeated multiplication (e.g., 54 = 5 × 5 × 5 × 5).
- Negative Exponents: Indicate repeated division. For example, 2-3 is the same as 1 / (23) = 1/8.
- Fractional Exponents: Represent roots. For example, 91/2 is the square root of 9, which is 3.
- Zero Exponent: Any non-zero number raised to the power of zero is 1 (e.g., 70 = 1).
Practical Applications
Exponents are fundamental in many fields, including science, engineering, computer science, and finance. They are used to describe:
- Compound interest growth in finance.
- Exponential growth or decay in biology (e.g., bacteria populations).
- Data storage units in computing (kilobytes, megabytes, gigabytes).
- Scientific notation for very large or very small numbers.