Exponents and Order of Operations

5 × 5 × 5 is written 5³, and read "five cubed" or "five to the power of three".

A warning worth repeating

5³ is 125, not 15. The exponent counts multiplications, not additions.

The order

Brackets first, then exponents, then multiply and divide, then add and subtract.

Ties are broken left to right

12 ÷ 3 × 2 is 8, because the division comes first when reading left to right.

The full order, now with exponents

Brackets first, then exponents, then multiplication and division left to right, then addition and subtraction left to right. Exponents slot in just after brackets, which is why 2 × 3² is 18 and not 36.

What an exponent means

3² means 3 × 3 = 9, and 3³ means 3 × 3 × 3 = 27. The exponent counts how many copies are multiplied, not what to multiply by. Writing 3² as 6 is the most common exponent error and it comes from reading the notation as multiplication.

Same-level operations go left to right

Multiplication and division sit at the same level, so 12 ÷ 3 × 2 is 8, not 2 — you work left to right. The same applies to addition and subtraction. Treating multiplication as always coming before division is a real and common misreading.

Use brackets to be clear

Even when the order rules make an expression unambiguous, adding brackets can make your intent obvious to a reader. Professional mathematicians and programmers both do this. Clarity is worth more than brevity in anything someone else will read.