Exponential Form: Exponentiation is a mathematical operation, 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:

$x^m\times x^n= x^{m+n}$

$\frac{x^m}{x^n}=x^{m-n}, \ where \ m>n \ and\ \frac{x^m}{x^n}=\frac{1}{x^{n-m}}, where \ n>m$

$(x^m)^n=x^{mn}$

$x^0=1$

$(xy)^m=x^my^n$

$(\frac{x}{y})^m=\frac{x^m}{y^m}$

$x^{-m}=\frac{1}{x^m} \ and\ \frac{1}{x^{-m}}=x^m$

$If x^m=x^n, \ then\ m=n, \ provided \ x>0 \ and \ x\neq 1$

$(x)^{\frac{m}{n}}=(x^m)^{\frac{1}{n}}=(x^{\frac{1}{n}})^m$