Order of Operations with Exponents
Squares and cubes inside longer expressions. Exponents come right after grouping symbols.
Where exponents fit
Exponents are the second step: after grouping symbols, before multiplication and division. An exponent applies only to the number or group directly in front of it, so 2 × 3² is 2 × 9 = 18, not 6² = 36.
On these sheets bases are 12 or less and exponents are 2 or 3. From grade 8 a base can be negative, and it is always written in parentheses: (−2)³ = −8.
Worked examples
- (3 − 1)2 + (10 + 4) = 18
- Parentheses: 3 − 1 = 222 + (10 + 4)
- Parentheses: 10 + 4 = 1422 + 14
- Exponents: 2² = 44 + 14
- Add: 4 + 14 = 1818
- [33 + (10 − 5)] + 2 = 34
- Parentheses: 10 − 5 = 5[33 + 5] + 2
- Parentheses, exponents: 3³ = 27[27 + 5] + 2
- Parentheses: 27 + 5 = 3232 + 2
- Add: 32 + 2 = 3434
Two more, answers only
- (68 − 23 × 7 − 6) + 4 = 10
- (5 × 5) × 62 = 900
More worksheets
Questions
When do you do exponents in the order of operations?
Right after grouping symbols. In 3 + 2³ × 4, first 2³ = 8, then 8 × 4 = 32, then 3 + 32 = 35. If the exponent sits on a group, as in (1 + 2)², finish the group first: 3² = 9.
Do the sheets use large powers?
No. Bases are 12 or less, and exponents are 2 or 3, so students can work them out without a calculator. Cubes use bases up to 5.
What can I do for free?
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