# Question #f5934

Jan 12, 2018

I've provide a list of 7 "laws" that I think you should be aware of.
However, as noted, you could derive more variations of these and some of them could be derived from others.

#### Explanation:

Here are the one's that I would consider essential:

• ${a}^{0} = 1$ provided $a \ne 0$
• ${a}^{1} = a$
• ${a}^{p + q} = {a}^{p} \cdot {a}^{q}$
• ${a}^{p \cdot q} = {\left({a}^{p}\right)}^{q} = {\left({a}^{q}\right)}^{p}$
• ${a}^{- b} = \frac{1}{{a}^{b}}$
• ${a}^{\frac{1}{b}} = \sqrt[b]{a}$

plus, more as a definition

• ${a}^{b} = c \Leftrightarrow {\log}_{a} c = b$

A few of these are derivable from others and you could extend this
by deriving different forms.