Conceptual Bridging: Laws of Indices

These laws apply for positive real bases \(a,b\) and real exponents. In the root formula, \(m\) is a positive integer.

1. \(a^m \times a^n = a^{m+n}\)
2. \(a^m \div a^n = a^{m-n}\)
3. \((a^m)^n = a^{mn}\)
4. \(a^m \times b^m = (ab)^m\)
5. \(\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m\)
6. \(a^0 = 1\)
7. \(\sqrt[m]{a} = a^{\frac{1}{m}}\)