$\sqrt[n]{xy} = \sqrt[n]{x} \cdot \sqrt[n]{y}$ for all real $x, y$

$\sqrt[n]{x^m} = (\sqrt[n]{x})^m$ for all real $x$ and positive integers $m, n$

$x^{-n} = \frac{1}{x^n}$ for all real $x \neq 0$ and positive integers $n$

$(x^a)^b = x^{ab}$ for all real $x$ and all real $a, b$