Soient \(a \in {\mathbb{R}^ + }\), \(b \in {\mathbb{R}^ + }\), \(n \in \mathbb{Q}\) et \(m \in \mathbb{Q}\).

1. \({a^m}{a^n} = {a^{m + n}}\)

2. \(\frac{{{a^m}}}{{{a^n}}} = {a^{m - n}}\)

3. \({\left( {ab} \right)^m} = {a^m}{b^m}\)

4. \({\left( {\frac{a}{b}} \right)^m} = \frac{{{a^m}}}{{{b^m}}}\)

5. \({\left( {{a^m}} \right)^n} = {a^{n.m}}\)

6. \({a^0} = 1\) avec \(a \ne 0\) et \({a^1} = a\)

7. \({a^{ - m}} = \frac{1}{{{a^m}}}\)

8. \({a^{ - \frac{m}{n}}} = \sqrt[n]{{{a^m}}}\)