PEMDAS, commonly known as the order of operations, is a fundamental principle in mathematics that ensures consistency and accuracy in evaluating mathematical expressions. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction, representing the sequence in which operations should be performed.

Here's how to apply PEMDAS:

**Parentheses:**Evaluate expressions within parentheses first. If there are nested parentheses, work from the innermost set outward.**Exponents:**Calculate any exponents or powers next.**Multiplication/Division:**Perform multiplication and division operations from left to right.**Addition/Subtraction:**Lastly, carry out addition and subtraction operations from left to right.

Let's illustrate the application of PEMDAS with the equation (5 + 8)^{2} × 6 ÷ 3 + 12 - 4

- Parentheses: Evaluate (5 + 8) = 13.
- Exponents: Square the result from step 1: 13
^{2}= 169. - Multiplication/Division: Calculate 169 × 6 = 1014, then divide by 3 = 338.
- Addition/Subtraction: Finally, perform the remaining operations: 338 + 12 - 4 = 346.