12.2 Important and useful rules/formulas

Exponents (assume each expression is defined.)

$a^n{a}^m=a^{n+m}$

$\frac{a^n}{a^m}=a^{n-m}$

${\left(a^n\right)}^m=a^{\mathrm{nm}}$

${\left(\mathrm{ab}\right)}^n=a^n{b}^n$

$a^{-1}=\frac{1}{a}$

$a^{-n}=\frac{1}{a^n}$

$a^0=1$

${\left(\frac{a}{b}\right)}^n=\frac{a^n}{b^n}$

Factorization and special product formulas

$\mathrm{ab}+\mathrm{ac}=a(b+c)$

$a^2+\mathrm{2ab}+b^2={(a+b)}^2$

$a^2-b^2=(a+b)(a-b)$

$a^2-\mathrm{2ab}+b^2={(a-b)}^2$

Formulas

$$\begin{array}{ll}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}& \text{Quadratic formula}\\ y=mx+b& \text{Slope-intercept form of a straight line}\\ y-y_1=m(x-x_1)& \text{Point-slope form of a straight line}\\ m=\frac{y_2-y_1}{x_2-x_1}& \text{Slope of a straight line passing through the points}(x_1,x_2)\text{and}(y_1,y_2)\end{array}$$