Exponential notation

Definition

Exponential notation is a mathematical method for representing numbers as a base raised to an exponent. It simplifies the expression and computation of very large or very small numbers.

5 Must Know Facts For Your Next Test

1. In exponential notation, the expression $a^b$ means 'a' is the base and 'b' is the exponent.
2. Any non-zero number raised to the power of zero equals one: $a^0 = 1$.
3. A negative exponent indicates a reciprocal: $a^{-b} = \frac{1}{a^b}$.
4. Multiplying exponential terms with the same base involves adding their exponents: $a^m \times a^n = a^{m+n}$.
5. Dividing exponential terms with the same base involves subtracting their exponents: $\frac{a^m}{a^n} = a^{m-n}$.

Review Questions

• What does the term $2^{-3}$ represent in standard form?
• How do you simplify $(3^2) \cdot (3^4)$ using exponential notation rules?
• Explain how you would convert $\frac{5^4}{5^2}$ into a single term with an exponent.

Related terms

Base: The number that is repeatedly multiplied in an exponential expression. In $3^4$, 3 is the base.

Exponent: Indicates how many times the base is multiplied by itself. In $3^4$, 4 is the exponent.

Scientific Notation: $A way of expressing numbers that are too large or too small to be conveniently written in decimal form, often using powers of ten.$