Exponents and Order of Operations Test Answer Key with Scoring – Grade 6

Question 1 Exponent basics (2 points)

(a) 3⁵ = 243 (9, 27, 81, 243).

(b) 2⁷ = 128.

Scoring: 1 point per part (the exponent form and value are both needed in (a)).

Question 2 Powers of 10 (2 points)

(a) Five zeros: 100,000.

(b) Four zeros: 10⁴.

Scoring: 1 point per part.

Question 3 Tiles as a power (2 points)

(a) 8². (b) 8 × 8 = 64 tiles.

Scoring: 1 point per part.

Question 4 Order matters (2 points)

(a) Divide first: 12 ÷ 3 = 4, then 30 − 4 = 26.

(b) Grouping first: 18 ÷ 3 = 6.

Scoring: 1 point per part.

Question 5 Power and subtraction (2 points)

4³ = 64 and 5 × 6 = 30, so 64 − 30 = 34.

Scoring: 1 point for 64, 1 point for the final answer.

Question 6 Multi-step expression (3 points)

Grouping: 11 − 3 = 8. Exponent: 8² = 64. Multiply and divide left to right: 2 × 64 = 128, then 128 ÷ 4 = 32. Add: 5 + 32 = 37.

Scoring: 1 point for grouping and exponent, 1 point for the multiply/divide steps, 1 point for the final answer.

Question 7 Spot the error (3 points)

(a) Jordan added 7 + 3 = 10 first and then multiplied by 4. Exponents and multiplication come before addition.

(b) 2² = 4, then 3 × 4 = 12, then 7 + 12 = 19.

Scoring: 1 point for (a); 1 point for the order in (b), 1 point for 19.

Question 8 Concert receipt (3 points)

(a) 4 × (12 + 3) − 6.

(b) 12 + 3 = 15; 4 × 15 = 60; 60 − 6 = $54.

Scoring: 1 point for the expression; 1 point for the order of steps, 1 point for $54.

Question 9 Power versus product (1 point)

The count is 3 × 3 × 3 = 3³ = 27. It is not 9 because three factors of 3 are multiplied, not just two.

Scoring: 1 point for both values and the comparison.