Powers

Some basic rules of powers: Here $a$, $b$, $x$, and $y$ are variables. (So for example $a^x$ with $a=3$ and $x=2$ means $3^2=9$.)

$$a^{-x} = \frac{1}{a^x}$$ (1)

$$\frac{1}{a^{-x}} = a^x$$ (2)

$$a^x \, a^y = a^{x+y}$$ (3)

$$(a^x)^y = a^{x\cdot y}$$ (4)

$$a^x\,b^y {\rm\;cannot\;be\;reduced!}$$ (5)