CHAPTER 1 KEY FORMULAS AND EQUATIONS

Commutative law of addition: $a + b = b + a$
Associative law of addition: $a + (b + c) = (a + b) + c$
Commutative law of multiplication: $a b = b a$
Associative law of multiplication: $a (b c) = (a b) c$
Distributive law: $a (b + c) = a b + a c$
$a + (- b) = a - b$ (1.1)
$a - (- b) = a + b$ (1.2)
$a^{m} \times a^{n} = a^{m + n}$ (1.3)
$\begin{matrix} \frac{a^{m}}{a^{n}} = a^{m - n} (m > n, a \neq 0), \\ \frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}} (m < n, a \neq 0) \end{matrix}$ (1.4)
${(a^{m})}^{n} = a^{m n}$ (1.5)
${(a b)}^{n} = a^{n} b^{n}, {(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}} (b \neq 0)$ (1.6)
$a^{0} = 1 (a \neq 0)$ (1.7)
$a^{- n} = \frac{1}{a^{n}} (a \neq 0)$ (1.8)
$\sqrt{a b} = \sqrt{a} \sqrt{b} (a and b positive real numbers)$ (1.9)

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans