Definition

1. Noun:
   • Exponent (mathematics): A number written above and to the right of another number (the base), indicating how many times the base is multiplied by itself. For example, in 2³, the number 3 is the exponent, meaning 2 × 2 × 2.

Usage Examples

• Noun:
  • Trong biểu thức 5⁴, số 4 là số mũ. (In the expression 5⁴, the number 4 is the exponent.)
  • Số mũ cho biết lũy thừa của cơ số. (The exponent indicates the power of the base.)
  • Anh ấy đang học về tính chất của số mũ. (He is studying the properties of exponents.)

Advanced Usage

• Exponential Function (Hàm số mũ): A mathematical function of the form f(x) = aˣ, where 'a' is a constant base and 'x' is the variable exponent.

  • Hàm số mũ được sử dụng rộng rãi trong khoa học và tài chính. (The exponential function is widely used in science and finance.)

• Exponential Growth (Tăng trưởng theo cấp số nhân/Tăng trưởng hàm mũ): A process that increases quantity over time at a rate proportional to its current value, often described using exponents.

  • Dân số có thể có tốc độ tăng trưởng hàm mũ. (A population can have a rate of exponential growth.)

Variants and Related Words

• Cơ số (Base): The number that is raised to a power by an exponent. In bⁿ, 'b' is the base.
• Lũy thừa (Power): The result of raising a base to an exponent. It refers to the whole expression (e.g., 2³) or its value (8).
• Hàm số mũ (Exponential function): As defined above.
• Số mũ nguyên (Integer exponent): An exponent that is an integer (whole number).
• Số mũ hữu tỉ (Rational exponent): An exponent that is a rational number (a fraction).

Synonyms

• Chỉ số (Index): Can be used in some mathematical contexts, similar to exponent.
• Lũy thừa (Power): While "lũy thừa" refers to the entire power operation or result, it is closely related and sometimes used in contexts involving the exponent.

Related Phrases/Compounds

• Phép tính lũy thừa (Exponentiation): The mathematical operation involving a base and an exponent.
• Luật số mũ (Laws of exponents): The rules governing operations with exponents (e.g., aᵐ × aⁿ = aᵐ⁺ⁿ).
• Phương trình mũ (Exponential equation): An equation in which the variable appears in the exponent.

1. (toán học) Exponent