exponentiation
Definition
Noun: 1. The mathematical operation of raising a base number to the power of an exponent: It is the process of repeated multiplication, where a number (the base) is multiplied by itself a certain number of times (the exponent). The result is called a power.
Usage
Exponentiation is a fundamental arithmetic operation. It is typically written as bⁿ, where b is the base and n is the exponent. For example, 2³ (read as "two to the power of three" or "two cubed") means 2 × 2 × 2.
Examples
- Noun:
- The expression
5⁴represents the exponentiation of 5 by 4. - In computer science, exponentiation is a common operation in cryptographic algorithms.
- Understanding exponentiation is essential before learning about logarithms.
Advanced Usage
- Properties of Exponentiation:
- Product of Powers:
bᵐ × bⁿ = bᵐ⁺ⁿ(When multiplying powers with the same base, add the exponents). - Power of a Power:
(bᵐ)ⁿ = bᵐˣⁿ(When raising a power to another power, multiply the exponents). - Zero Exponent: Any non-zero base raised to the power of zero equals one:
b⁰ = 1.
Variants and Related Words
- Exponent (n): The number that indicates how many times the base is used as a factor (e.g., the in ).
- Base (n): The number that is raised to a power (e.g., the in ).
- Power (n): The result of an exponentiation operation (e.g., is the power of ).
Synonyms
- Raising to a power: The act of performing exponentiation.
- Involution: A less common synonym for exponentiation.
Related Phrases and Concepts
- Exponential Growth: A rapid increase characterized by a constant multiplicative rate, modeled by exponentiation.
- Exponential Function: A function of the form , where the base is a constant and the exponent is a variable.
Noun
-
the process of raising a quantity to some assigned power
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