Exponents and Order of Operations Worksheet Answer Key – Grade 6

Problem 1 Repeated multiplication

Three factors of 6: 6³ = 6 × 6 × 6 = 36 × 6 = 216.

Problem 2 Evaluating powers

3⁴ = 3 × 3 × 3 × 3 = 81. 7² = 49. 2⁶ = 64. 10³ = 1,000. 81, 49, 64, 1,000.

Problem 3 Writing with exponents

Count the factors. (a) 9³ (b) 5⁵ (c) 1.5².

Problem 4 Square floor

There are 7 rows of 7 tiles.

7² = 49 tiles.

Problem 5 Powers of 10

The exponent counts the zeros. 10² = 100, 10⁴ = 10,000, 10⁶ = 1,000,000.

Problem 6 Powers of 10 from numbers

100,000 has 5 zeros and 10,000,000 has 7 zeros. 10⁵ and 10⁷.

Problem 7 Left to right

Subtraction and addition share a level, so go left to right: 18 − 6 = 12, then 12 + 4 = 16.

Problem 8 Multiplication first

5 + 3 × 7 = 5 + 21 = 26. (5 + 3) × 7 = 8 × 7 = 56. 26 and 56; the parentheses force the addition to happen first.

Problem 9 Division and exponent

(a) Left to right: 40 ÷ 5 = 8, then 8 × 2 = 16. (b) Exponent first: 2³ = 8, then 9 + 8 = 17. (a) 16 (b) 17.

Problem 10 Power and subtraction

Powers: 5² = 25 and 2³ = 8. Multiply: 6 × 3 = 18. Then 25 + 18 − 8 = 35.

Problem 11 Grouping and exponent

Grouping: 10 − 4 = 6. Exponent: 6² = 36. Left to right: 6 × 36 = 216, and 216 ÷ 9 = 24.

Problem 12 Find the error

The student added first: 8 + 2 = 10, then 10 × 5 = 50. Multiplication must come first: 2 × 5 = 10, then 8 + 10 = 18.

Problem 13 Parentheses with a power

Grouping: 2 + 3 = 5. Exponent: 5² = 25. Multiply: 3 × 25 = 75. Subtract: 100 − 75 = 25.

Problem 14 Crate of blocks

Each layer has 3 × 3 = 9 blocks and there are 3 layers: 9 × 3 = 27. 3³ = 27 blocks.

Problem 15 Spreading news

Day 1: 3¹, day 2: 3² = 9, and each day multiplies by 3. Day 5 is 3⁵ = 3 × 3 × 3 × 3 × 3 = 243 people.

Problem 16 Growing culture

Doubling 6 times multiplies by 2⁶ = 64. Expression: 5 × 2⁶ = 5 × 64 = 320 cells.

Problem 17 Stadium seats

Ten times as many adds one factor of 10: 10⁶. 10⁵ = 100,000 and 10⁶ = 1,000,000. Stadium 10⁵ = 100,000; arena 10⁶ = 1,000,000.

Problem 18 Food truck bill

Total before coupon: 8 × 3 + 5 × 2 = 24 + 10 = 34. Expression: (8 × 3 + 5 × 2 − 4) ÷ 2 = (24 + 10 − 4) ÷ 2 = 30 ÷ 2. Each friend pays $15.

Problem 19 Two-part expressions

(a) 3² − 1 = 8; 8² = 64; 64 ÷ 8 = 8; 4 + 8 = 12. (b) (3 + 4) × 5 − 2 = 7 × 5 − 2 = 35 − 2 = 33. (a) 12 (b) (3 + 4) × 5 − 2.

Problem 20 Tiles with a rug

The room has 9² = 81 tiles and the rug covers 4² = 16.

81 − 16 = 65 tiles, from the expression 9² − 4².