# 12.3: Important and Useful Rules/Formulas

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## Exponents (Assume each expression is defined.)

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

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

$$(a^n)^m = a^{nm}$$

$$(ab)^n = a^nb^n$$

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

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

$$a^0 = 1$$

$$(\dfrac{a}{b})^n = \dfrac{a^n}{b^n}$$

## Factorization and special product formulas

$$ab + ac = a(b + c)$$

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

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

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

## Formulas

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

This page titled 12.3: Important and Useful Rules/Formulas is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .