Aus Online Mathematik Brückenkurs 1

The number 4 can be written as \displaystyle 4=2\centerdot 2=2^{2} and then, using the power rules, we obtain

\displaystyle 4^{\frac{1}{2}} = \bigl(2^{2}\bigr)^{\frac{1}{2}} = 2^{2\cdot \frac{1}{2}} = 2^{1} =2\,.

Note: Another way to denote \displaystyle 4^{\frac{1}{2}} is \displaystyle \sqrt{4} (the square root of 4); more on this in the section on roots later in the course.