What Are Exponents?
Exponents are a way to write repeated multiplication in a shorter form.
$2^3 = 2 \times 2 \times 2 = 8$
Parts of an Exponent
In $a^n$:
- a is the base (the number being multiplied)
- n is the exponent (how many times to multiply it)
Example: $5^4 = 5 \times 5 \times 5 \times 5 = 625$
Important Rules
- $a^1 = a$ (anything to the power 1 is itself)
- $a^0 = 1$ (any non-zero number to the power 0 is 1)
- $a^m \cdot a^n = a^{m+n}$
- $$\frac{a^m}{a^n} = a^{m-n}$$
- $$(a^m)^n = a^{m \cdot n}$$
Why Are Exponents Useful?
They let us write large numbers or repeated multiplication easily. For example:
$10^6 = 1,000,000$
Also used in scientific notation, physics, and computing.
Quick Practice
- $3^2 = \ ?$
- $2^5 = \ ?$
- $(4^2)^2 = \ ?$