1.6 Exponent Rules

Notes

An exponent tells how many times a base is multiplied by itself: $x^4 = x \cdot x \cdot x \cdot x$.

• Product rule: $x^a \cdot x^b = x^{a+b}$. Quotient rule: $\displaystyle \frac{x^a}{x^b} = x^{a-b}$.
• Power rule: $(x^a)^b = x^{ab}$ and $(xy)^a = x^a y^a$.
• Zero exponent: $x^0 = 1$ for $x \neq 0$. Negative exponent: $\displaystyle x^{-n} = \frac{1}{x^n}$.
• Example: $(3a^2)^2 = 9a^4$. Coefficients are squared too.