The following examples illustrate entry of some common expressions.
Expression 
Do this 
To display this 

A simple expression with integers 
Type 2x+52500 
$2x+52500$ 
A polynomial with a fractional coefficient 

$\frac{1}{2}{x}^{2}+4x+2$ 
A simple inequality 
Type x>=4 
$x\ge 4$ 
Set notation with fractions 

$\left(\frac{1}{9},\frac{2}{7},\frac{3}{5}\right)$ 
A square root 

$\sqrt{x}$ 
A cube root 

$\sqrt[3]{x}$ 
An expression involving pi and Euler's number 

$\pi +{\mathit{e}}^{2}$ 
The natural logarithm of an absolute value 

$\mathrm{ln}\left(\leftx\right\right)$ 
An inverse sine 
Although you could type arcsin or use the tool button, this example illustrates how you can enter certain functions using the keyboard alone. 
${\mathrm{sin}}^{1}\left(x\right)$ 
A complex number 

$2+3\mathit{i}$ 
A vector in vector bracket form 

$\u27e812,15,22\u27e9$ 
A vector in bold ijk form 

$5\mathbf{i}+24\mathbf{j}+4\mathbf{k}$ 