$${a^{m} \bullet a^{n} = a^{m + n}}{a^{n}:a^{m} = a^{m - n}\ dla\ n \geq m}{{{(a}^{n})}^{m} = a^{n \bullet m}}{a^{n} \bullet b^{n} = \left( a \bullet b \right)^{n}}{\frac{a^{n}}{b^{n}} = \left( \frac{a}{b} \right)^{n}}{a^{0} = 1}{\sqrt[n]{a \bullet b} = \sqrt[n]{a} \bullet \sqrt[n]{b}}{\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}\ b > 0}{\sqrt[m]{\sqrt[n]{a}} = \sqrt[{n \bullet m}]{a}}{\left( \sqrt[n]{a} \right)^{p} = \sqrt[n]{a^{p}}}{\left( \sqrt[n]{a} \right)^{n} = a}{\left( a + b \right)^{2} = a^{2} + 2ab + b^{2}}{\left( a - b \right)^{2} = a^{2} - 2ab + b^{2}}{a^{2} - b^{2} = \left( a - b \right)\left( a + b \right)}{\left( a + b \right)^{3} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3}}{\left( a - b \right)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}}{a^{3} + b^{3} = \left( a + b \right)\left( a^{2} - ab + b^{2} \right)}{a^{3} - b^{3} = \left( a - b \right)\left( a^{2} + ab + b^{2} \right)}{a^{- n} = \frac{1}{a^{n}}}{\frac{1}{a^{n}} = \left( \frac{1}{a} \right)^{n}a \neq 0\ i\ n \in N\backslash n}{a^{\frac{1}{n}} = \sqrt[n]{a}\backslash n}{a^{- \frac{m}{n}} = a^{\frac{1}{\frac{m}{n}}}\backslash n}{{\sqrt{a}}^{2} = 0\backslash n}{\sqrt{a^{2}} = \left| a \right|\backslash n}{\frac{7}{\sqrt{3}} = \frac{7\sqrt{3}}{\sqrt{3} \bullet \sqrt{3}} = \frac{7\sqrt{3}}{3}\backslash n}{\frac{7}{2 - \sqrt{3}} = \frac{7(2 + \sqrt{3})}{(2 - \sqrt{3})(2 + \sqrt{3})}\backslash n}$$