$$\mathbf{Potencias}$$ $$\underbrace{a \cdot a \cdots a}_{\hbox{n veces}} = a^n$$ $$a^0=1$$ $$a^1=a$$ $$a^n \cdot a^m = a^{n+m}$$ $$\frac{a^n}{a^m} = a^{n-m}$$ $$(a^n)^m = a^{n \cdot m}$$ $$a^{-n} = \frac{1}{a^n}$$ $$a^n \cdot b^n = (a \cdot b)^{n}$$ $$\left( \frac{a}{b} \right)^{n} = \frac{a^n}{b^n}$$ $$\left( \frac{a}{b} \right)^{-n} = \frac{b^n}{a^n}$$ $$\mathbf{Radicales}$$ $$\sqrt[n]{a} = a^{\frac{1}{n}}$$ $$\frac{1}{\sqrt[n]{a}} = a^{-\frac{1}{n}}$$ $$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$ $$\frac{1}{\sqrt[n]{a^m}} = a^{-\frac{m}{n}}$$ $$\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{a \cdot b}$$ $$\frac{\sqrt[n]{a}}{\sqrt[n]{b}} = \sqrt[n]{\frac{a}{b}}$$ $$\sqrt[m]{\sqrt[n]{a}} = \sqrt[n \cdot m]{a}$$ $$\left( \sqrt[n]{a} \right)^{m} = \sqrt[n]{a^m}$$ $$\sqrt[n]{a^n} = a$$ $$\sqrt[n \cdot p]{a^p} = \sqrt[n]{a}$$ $$a\sqrt[n]{b} = \sqrt[n]{a^n b}$$ $$a\sqrt[n]{c} \pm b\sqrt[n]{c} = (a \pm b)\sqrt[n]{c}$$ $$\frac{a}{\sqrt{b}}=\frac{a}{\sqrt{b}} \cdot \frac{\sqrt{b}}{\sqrt{b}} = \frac{a \sqrt{b}}{b}$$ $$\frac{a}{\sqrt[n]{b^m}} = \frac{a}{\sqrt[n]{b^m}} \cdot \frac{\sqrt[n]{b^{n-m}}}{\sqrt[n]{b^{n-m}}} = \frac{a\sqrt[n]{b^{n-m}}}{b}$$ $$\mathbf{Logaritmos}$$ $$\log_{a}{b} = x \Leftrightarrow a^x = b$$ $$\log_{a}{1} = 0$$ $$\log_{a}{a} = 1$$ $$\log_{a}{a^n} = n$$ $$\log_{a}{(x \cdot y)} = \log_{a}{x} + \log_{a}{y}$$ $$\log_{a}{\left( \frac{x}{y} \right)} = \log_{a}{x} - \log_{a}{y}$$ $$\log_{a}{x^n} = n \log_{a}{x}$$ $$\log_{a}{\sqrt[n]{x}} = \frac{1}{n} \log_{a}{x}$$ $$\log_{a}{x} = \frac{\log_{b}{x}}{\log_{b}{a}} \hbox{ (Cambio de base)}$$ $$\log_{10}{x} = \log{x} \hbox{ (Logaritmo decimal)}$$ $$\log_{e}{x} = \ln{x} \hbox{ (Logaritmo neperiano)}$$