Question
What are exponents?
Answers
Answered by
GPT-4o mini
Exponents are a mathematical notation used to indicate how many times a number, called the base, is multiplied by itself. The exponent is written as a small number above the base. For example, in the expression \(a^n\):
- \(a\) is the base.
- \(n\) is the exponent.
This means you multiply the base \(a\) by itself \(n\) times.
For example:
- \(2^3\) (which reads as "two raised to the power of three") equals \(2 \times 2 \times 2 = 8\).
- \(5^2\) equals \(5 \times 5 = 25\).
Exponents have several important properties, including:
1. **Multiplication of Powers**: \(a^m \times a^n = a^{m+n}\)
2. **Division of Powers**: \(a^m \div a^n = a^{m-n}\) (where \(a \neq 0\))
3. **Power of a Power**: \((a^m)^n = a^{m \times n}\)
4. **Zero Exponent**: \(a^0 = 1\) (where \(a \neq 0\))
5. **Negative Exponent**: \(a^{-n} = \frac{1}{a^n}\) (where \(a \neq 0\))
Exponents can also be extended to rational numbers (e.g., \(a^{1/n}\) represents the nth root of \(a\)) and real numbers in more advanced mathematics.
- \(a\) is the base.
- \(n\) is the exponent.
This means you multiply the base \(a\) by itself \(n\) times.
For example:
- \(2^3\) (which reads as "two raised to the power of three") equals \(2 \times 2 \times 2 = 8\).
- \(5^2\) equals \(5 \times 5 = 25\).
Exponents have several important properties, including:
1. **Multiplication of Powers**: \(a^m \times a^n = a^{m+n}\)
2. **Division of Powers**: \(a^m \div a^n = a^{m-n}\) (where \(a \neq 0\))
3. **Power of a Power**: \((a^m)^n = a^{m \times n}\)
4. **Zero Exponent**: \(a^0 = 1\) (where \(a \neq 0\))
5. **Negative Exponent**: \(a^{-n} = \frac{1}{a^n}\) (where \(a \neq 0\))
Exponents can also be extended to rational numbers (e.g., \(a^{1/n}\) represents the nth root of \(a\)) and real numbers in more advanced mathematics.