A power:

$$a^b$$

consists of a base $a$ and an exponent $b$. The base $a$ is the number that is to be multiplied with itself $b$ times.

$$\begin{array}{cc}{a}^b=\underset{b\text{ times}}{\underbrace{a\cdot a\cdot a\cdots a}}& \\ \underset{b\text{ times}}{\underbrace{\sqrt[b]{a}\cdot \sqrt[b]{a}\cdot \sqrt[b]{a}\cdots \sqrt[b]{a}}}={\left(\sqrt[b]{a}\right)}^b=a& \end{array}$$

Note! $\frac{1}{a}=a^{-1}$

Pay special attention to the fact that $\sqrt{a}=a^{\frac{1}{2}}$. This is called the square root of $a$. It then follows that $\sqrt[n]{a}=a^{\frac{1}{n}}$. This is called the $n$th root of $a$.

If $n$ is an even number, you get an even root. Some examples include $\sqrt[4]{a},\sqrt[6]{a},\sqrt[8]{a},\dots$

In the same way, you get odd roots when $n$ is an odd number. They look like this: $\sqrt[3]{a},\sqrt[5]{a},\sqrt[7]{a},\dots$

The difference between even and odd roots is that even roots are only defined for $a\ge 0$. In odd roots, $a$ can be either positive or negative.

Note! You can not take the even root of a negative number. $\sqrt[4]{-2}=$ is undefined!

Note! When you have a negative exponent, it’s usually best to write the power as a fraction. The reason to do this is that in general, positive exponents are much easier to deal with than negative ones.