Exponent

Definition

An exponent refers to the number that indicates how many times a base number is multiplied by itself. It is typically written as a small number to the upper right of the base number.

5 Must Know Facts For Your Next Test

1. The expression $a^n$ means 'a' is multiplied by itself 'n' times.
2. Any non-zero number raised to the power of zero equals one, i.e., $a^0 = 1$ for $a \neq 0$.
3. When multiplying like bases, you add the exponents: $a^m \times a^n = a^{m+n}$.
4. When dividing like bases, you subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$ for $a \neq 0$.
5. Raising an exponent to another exponent involves multiplying the exponents: $(a^m)^n = a^{mn}$.

Review Questions

• What does the expression $3^4$ represent in terms of multiplication?
• How do you simplify $(2^3)^2$ using properties of exponents?
• What is the value of any non-zero number raised to the power of zero?

Related terms

Base: The number that is being multiplied by itself when raised to an exponent.

Exponentiation: The mathematical operation involving raising a base to an exponent.

Power: The result of raising a base to an exponent, often used interchangeably with 'exponent'.