exponentiation

Thân thiện

A student writes an exponentiation problem on the chalkboard.

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 5⁴ represents 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.

Học thuật

Noun

1. the process of raising a quantity to some assigned power

Từ đồng nghĩa

• involution