Taking both sides of an equation to any power

This means that if we know that $q = a z^2$ that we also know that:

$$q^{n} = (a z^2)^n$$

for any real number $n$ where the parentheses are necessary. We will more about powers below - they have special rules for tranforming the latter term into $a^n z^{2n}$ (for example).

Knowing the ``special'' rules for powers is especially important if the original equation can take on negative or complex values or has any sort of domain restrictions. Nevertheless, this is a very powerful transformation and one uses it quite often in solving problems. This rule will usually work even if the quantities have units.