What is the correct order of operations when simplifying a numerical expression?

The correct order of operations is essential for accurately simplifying numerical expressions and solving mathematical problems. The widely accepted sequence is: first, handle operations inside grouping symbols (like parentheses), then evaluate exponents, followed by performing multiplication and division from left to right, and finally addressing addition and subtraction also from left to right.

In this context, starting with grouping symbols ensures you deal with the most crucial parts of the expression that may affect all subsequent calculations. After that, evaluating exponents allows you to simplify powers before introducing multiplication or division, which operates at the same level of priority, followed by addition and subtraction, which are the last operations to be resolved.

This order ensures consistency and correctness in mathematical reasoning. Therefore, the sequence of Grouping Symbols, Exponents, Multiplication and Division, Addition and Subtraction accurately reflects the standardized procedure used in mathematics to avoid ambiguity in calculations.