Exponent Rules Formula

The Formula

When to use: Since $a^3 = a \cdot a \cdot a$ and $a^2 = a \cdot a$, multiplying them gives $a \cdot a \cdot a \cdot a \cdot a = a^5$. You just add the counts. All the other rules follow the same logic of counting how many times you multiply.

Quick Example

Notation

What This Formula Means

A set of laws governing how exponents behave under multiplication, division, and raising to a power: product rule ($a^m \cdot a^n = a^{m+n}$), quotient rule ($a^m / a^n = a^{m-n}$), power rule ($(a^m)^n = a^{mn}$), zero exponent ($a^0 = 1$ for $a \neq 0$), and negative exponent ($a^{-n} = \frac{1}{a^n}$).

Since $a^3 = a \cdot a \cdot a$ and $a^2 = a \cdot a$, multiplying them gives $a \cdot a \cdot a \cdot a \cdot a = a^5$. You just add the counts. All the other rules follow the same logic of counting how many times you multiply.