LAW OF EXPONENTS
\(\begin{array}{l}{1.\:\:\: \left ({{a^m}} \right)^n} = {a^{mn}} \\2.\:\:\:{a^m}\left( {{a^n}} \right) = {a^{m + n}} \\3.\:\:\:\frac{{{a^m}}}{{{a^n}}} = {a^{m - n}} = \frac{1}{{{a^{n - m}}}} \\4.\:\:\:{\left( {ab} \right)^n} = {a^n}{b^n} \\5.\:\:\:{\left( {{a^m}} \right)^{\frac{n}{p}}} = {a^{\frac{{mn}}{p}}} \\6.\:\:\:{a^{\frac{m}{n}}} = \sqrt[n]{{{a^m}}} \\7.\:\:\:{a^n} = \frac{1}{{{a^{ - n}}}} \\8.\:\:\:\frac{1}{{{a^m}}} = {a^{ - m}} \\9.\:\:\:{\left( {\frac{a}{b}} \right)^n} = \frac{{{a^n}}}{{{b^n}}} \\10.\:\:\:{a^0} = 1,\: where\: a\: ≠\: 0\end{array}\)