Take a look at the applet: Power Functions
If $y$ is directly proportional to a power of $x$, so $y=c\cdot {x}^{p}$, then this is called a power function. The constant $c$ is called the proportionality constant.
You can look at a few examples of power functions here. In these functions, $p$ is always positive or $0$ and $c=1$.
There are two ways to reverse the calculation in a power function $y={x}^{p}$ (thus with $c=1$ ):
$x=\sqrt[p]{y}$
$x={y}^{\frac{1}{p}}$
Depending on the value of
$p$ you can get one or two values for x.
If the proportionality factor has a value other than
$1$, then you have to start with dividing by
$c$. From there you can either apply the root of power
$p$, or use the inverse power.
The rules for working with powers (see: "Exponential functions" ) are valid here, too!
For every $x$ and any real numbers $a$ en $b$ the following properties of powers and exponents apply:
${x}^{0}=1$
${x}^{\mathrm{-}a}=\frac{1}{{x}^{a}}$ as long as $x=!0$
${x}^{\frac{1}{a}}=\sqrt[a]{x}$ as long as $x\ge 0$ en $a>0$.
${x}^{a+b}={x}^{a}\cdot {x}^{b}$
${x}^{a-b}=\frac{{x}^{a}}{{x}^{b}}$ as long as $x=!0$
${\left({x}^{a}\right)}^{b}={x}^{a\cdot b}$