Exponent Rules

Given expression:



2^5 $$

and



x^n $$

It is actually



2^5=\underbrace{2\cdot2\cdot2\cdot2\cdot2\cdot2}_\text{5 times} $$

and similar



x^n=\underbrace{x\cdot x\cdot x\cdot\ldots\cdot x}_\text{n times} $$

While we write these expression,

x\to $$ the number at the bottom is called the base



n\to $$ the number at the top, how many the base multiplying by itself, is called the exponent or power

The Product Rule


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

$$ \begin{array}{lcl} \text{multiplying the exponents} \\ \text{with the same base} \end{array} \to \mbox{add the exponents} $$

For example: