The order of operations outlines an order we should follow to evaluate expressions with multiple operations. We often use PEMDAS to remember the order of operations:
The "exponents" part of PEMDAS also includes radicals. We don't typically include "radicals" in the acronym, because all radicals can be written as exponents (fractional exponents, specifically). So as long as we remember that exponents and radicals are related, we can remember to evaluate both exponents and radicals after parentheses, but before multiplication, division, addition, and subtraction.
Let's focus first on evaluating expressions containing exponents:



Evaluate  

Evaluate  

Our Solution  
 



Evaluate first  

Then multiply by  

Our Solution 
When we encounter radicals (roots, such as square roots or cube roots), we treat them as being on the same level as exponents in the order of operations, and evaluate them before multiplication, division, addition and subtraction. This is illustrated in the examples below:



Evaluate the square root first  

Then multiply by  

Our Solution  
 



Evaluate the square root first  

Then multiply by  

Our Solution 
What do we do when an expression contains both exponents and radicals? Because exponents and radicals are at the same level according to the order of operations, we can think of their relationship being like multiplication and division, or addition and subtraction: we evaluate exponents and radicals as we see them reading left to right.



Evaluate the square root first  

Then evaluate the exponent  

Multiply by  

Our Solution 