Order of operations with powers and roots · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Powers, roots, and the order of operations

Mathematics · Multiplication & Division · ages 11-12
Name ______________________   Date ____________

  1. Sam works out 2 + 3 × 4 by going left to right: 2 + 3 = 5, then 5 × 4 = 20. Maria follows the order of operations: 3 × 4 = 12 first, then 2 + 12 = 14. Why is Maria's answer the correct one?

    • Multiplication has to be done before addition
    • Sam made a typing mistake
    • Both answers are correct
    • Addition always comes before multiplication

  2. Which step do you do first in 5 + 2³ ÷ 4?

    • Add 5 and 2
    • Work out 2³
    • Divide by 4

  3. In order of operations, powers are worked out before multiplication and division.

    Circle one:   True   False

  4. What is the reciprocal of 3?

    • 3
    • 1/3
    • -3

  5. Work out 4^2 - |2 × (-5)|.

    Answer: ______________

  6. Work out (8 - 5)^2 - (5 - 8)^2.

    Answer: ______________

  7. Work out 10 - (-3)^3.

    Answer: ______________

  8. Work out 10 - (-3)^2.

    Answer: ______________

  9. Work out (2 × 3)^2 - 2 × 3^2.

    Answer: ______________

  10. Zara says (2 + 3)² = 2² + 3² = 4 + 9 = 13. What is her mistake?

    • She split the power over the addition instead of adding first
    • She forgot to multiply 2 and 3
    • She should have divided before squaring
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Powers, roots, and the order of operations W1-mt_X5cypSGoGU-s1

  1. Multiplication has to be done before addition · The order of operations says to multiply and divide before you add and subtract. That rule is what makes sure everyone gets the same answer for the same expression.
  2. Work out 2³ · Powers (indices) are solved right after brackets, before you divide or add. 2³ = 8 comes before ÷4 or +5.
  3. True · Powers (indices) come right after brackets, before multiply, divide, add, or subtract.
  4. 1/3 · The reciprocal flips 3 into 1/3, and 3 × 1/3 = 1.
  5. 6 · Solve inside the absolute value bars and the power before subtracting.
  6. 0 · Solve inside each set of brackets first, then square each result before subtracting.
  7. 37 · An odd power keeps the negative sign, so (-3)^3 stays negative, and subtracting a negative number is the same as adding.
  8. 1 · Powers are solved before subtraction, and squaring a negative number gives a positive result.
  9. 18 · These two parts look similar but are different: one squares the whole bracket, the other squares just the 3 before multiplying by 2.
  10. She split the power over the addition instead of adding first · Brackets come first: 2 + 3 = 5, then square it: 5² = 25. A power cannot be split over addition like that.
Worksheet · LightMySky