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Powers, roots and the order of operations
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Powers are a short way to write repeated multiplying. The order of operations makes sure everyone gets the same answer.
Powers and roots
52 = 5 × 5 = 25 (5 squared). 23 = 2 × 2 × 2 = 8 (2 cubed).
The square root undoes squaring: √49 = 7. The cube root undoes cubing: ∛27 = 3.
Learn the powers of 2: 2, 4, 8, 16, 32, 64 ...
The square root undoes squaring: √49 = 7. The cube root undoes cubing: ∛27 = 3.
Learn the powers of 2: 2, 4, 8, 16, 32, 64 ...
Order of operations
Brackets, then Indices (powers and roots), then Division and Multiplication (left to right), then Addition and Subtraction (left to right).
3 + 4 × 2 = 3 + 8 = 11
(3 + 4) × 2 = 7 × 2 = 14
3 + 4 × 2 = 3 + 8 = 11
(3 + 4) × 2 = 7 × 2 = 14
Reciprocals
The reciprocal of a number is 1 divided by it.
The reciprocal of 4 is 14. The reciprocal of 23 is 32.
A number times its reciprocal is 1.
The reciprocal of 4 is 14. The reciprocal of 23 is 32.
A number times its reciprocal is 1.
Work out 20 − 32 × 2.
- Indices first: 32 = 9
- Then multiply: 9 × 2 = 18
- Then subtract: 20 − 18 = 2
Answer: 2
Powers mean repeated multiplying; roots undo them. Follow BIDMAS: brackets, indices, then × and ÷, then + and −.
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