CHAPTER 11 KEY FORMULAS AND EQUATIONS

Exponents	$a^{m} \times a^{n} = a^{m + n}$ (11.1) $\frac{a^{m}}{a^{n}} = a^{m - n} or \frac{a^{m}}{a^{n}} = \frac{1}{a^{n - m}} (a \neq 0)$ (11.2) ${(a^{m})}^{n} = a^{m n}$ (11.3) ${(a b)}^{n} = a^{n} b^{n}, {(\frac{a}{b})}^{n} = \frac{a^{n}}{b^{n}} (b \neq 0)$ (11.4) $a^{0} = 1 (a \neq 0)$ (11.5) $a^{- n} = \frac{1}{a^{n}} (a \neq 0)$ (11.6)
Fractional exponents	$a^{1 / n} = \sqrt[n]{a}$ (11.7) $a^{m / n} = \sqrt[n]{a^{m}} = {(\sqrt[n]{a})}^{m}$ (11.8)
Radicals	$\sqrt[n]{a^{n}} = {(\sqrt[n]{a})}^{n} = a$ (11.9) $\sqrt[n]{a} \sqrt[n]{b} = \sqrt[n]{a b}$ (11.10) $\sqrt[m]{\sqrt[n]{a}} = \sqrt[m n]{a}$ (11.11) $\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}} (b \neq 0)$ (11.12)

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