AI Tutor
If you type 2+3×42 + 3 \times 4 into a basic four-function calculator, it might display 2020, but a scientific calculator gives 1414.
Without a universal agreement on which operation happens first, the exact same mathematical sentence produces two completely different answers.

The Hierarchy of Operations

The order of operations ranks mathematical actions by their compression power: exponents represent repeated multiplication, and multiplication represents repeated addition, so higher-level operations take priority.
In the early 1900s, textbook authors and mathematicians formalized these conventions so that engineers and scientists across the globe could evaluate formulas with identical results.
Grouping symbols like parentheses ( )( \ ), brackets [ ][ \ ], and fraction bars act as shields that override standard ranking, forcing you to evaluate everything inside them first.
How do these four tiers play out when an expression combines exponents, parentheses, and arithmetic all at once?

Step-by-Step Evaluation

Consider the expression 4+2×(32−1)4 + 2 \times (3^2 - 1). We simplify from the innermost level outward, starting inside the parentheses.
Inside the parentheses, the exponent 323^2 took priority over subtraction, turning 32−13^2 - 1 into 9−1=89 - 1 = 8 before multiplication took place.
What happens when grouping symbols are nested inside each other, or hidden in a division bar?