Exponential Form: Exponentiation is a , written as $b^n$, involving two numbers, the base $b$ and the exponent $n$. When $n$ is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is $b^n$, is the product of multiplying $n$ bases: $b^n=b\times b\times b\times ... \times b$

In that case, $b^n$, is called the $n^{th}$ power of $b$, or $b$ raised to the power $n$.

When $n$ is a negative integer and $b$ is not zero, $b^{-n}$  is naturally defined as $\frac{1}{b^n}$

Note:

1. If $\frac{p}{q}$ is a rational number, then $(\frac{p}{q})^m$ $=$ $\frac{p^m}{q^m}$
2. Reciprocal of $\frac{p}{q}$ is $\frac{q}{p}$, where $p\neq 0$ and $q\neq 0$
3. Let $x$ be any non-zero real number and $m$ and $n$ be positive integers: $x^m\times x^n= x^{m+n}$ $\frac{x^m}{x^n}$ $=x^{m-n}$ , where $m>n$ and $\frac{x^m}{x^n}$ $=$ $\frac{1}{x^{n-m}}$, where $n>m$ $(x^m)^n=x^{mn}$ $x^0=1$ $(xy)^m=x^my^n$ $(\frac{x}{y})^m$ $=$ $\frac{x^m}{y^m}$ $x^{-m} =$ $\frac{1}{x^m}$  and $\frac{1}{x^{-m}}$ $= x^m$

If $x^m=x^n$,  then $m=n$,  provided $x>0$ and $x\neq 1$ $(x)^{\frac{m}{n}}=(x^m)^{\frac{1}{n}}=(x^{\frac{1}{n}})^m$