Exponents and Order of Operations: Grade 6 Math Test Answer Key – PDF Download

Question 1: Evaluating Powers (2 points)

1. \(4^3 = 4\times 4\times 4 = 16\times 4 = \) \(64\)
2. \(10^5\) is a 1 followed by five zeros: 100,000

Scoring: 1 point for each correct part. Give 0 for part (a) if the answer is \(12\) (multiplying 4 by 3).

Question 2: Using an Exponent (2 points)

Four factors of 6: \(6^4\). Then \(6^2 = 36\), \(6^3 = 216\), \(6^4 = 216\times 6 = \) \(1,296\)

Scoring: 1 point for \(6^4\); 1 point for 1,296.

Question 3: Addition, Subtraction, Multiplication, Division (2 points)

1. Multiply first: \(4\times 5 = 20\). Then \(28 – 20 + 6 = 8 + 6 = \) \(14\)
2. Left to right: \(48: 8 = 6\), then \(6\times 3 = \) \(18\)

Scoring: 1 point for each correct part. Answers of \(34\) for (a) or \(2\) for (b) earn 0 points.

Question 4: Grouping Symbols (2 points)

1. Parentheses: \(15 – 7 = 8\). Left to right: \(8\times 4 = 32\), then \(32: 2 = \) \(16\)
2. Parentheses: \(4+6 = 10\). Divide: \(60: 10 = 6\). Subtract: \(6 – 2 = \) \(4\)

Scoring: 1 point for each correct part.

Question 5: Effect of Parentheses (2 points)

1. Exponent: \(3^2 = 9\). Multiply: \(9\times 2 = 18\). Add: \(7 + 18 = \) \(25\)
2. Parentheses: \(7+3 = 10\). Exponent: \(10^2 = 100\). Multiply: \(100\times 2 = \) \(200\)

Scoring: 1 point for each correct part.

Question 6: Multi-Step Expressions (3 points)

1. Inside parentheses, exponent first: \(2^3 = 8\), so \(8 + 4 = 12\). Then \(5\times 12 = 60\) and \(60 – 9 = \) \(51\)
2. Parentheses: \(13 – 4 = 9\). Divide: \(90: 9 = 10\). Exponent: \(3^2 = 9\). Add: \(10 + 9 = \) \(19\)
3. Exponents: \(2^4 = 16\) and \(2^2 = 4\). Multiply: \(3\times 4 = 12\). Subtract: \(16 – 12 = \) \(4\)

Scoring: 1 point for each correct part.

Question 7: Comparing Powers (2 points)

1. \(2^6 = 64\) and \(6^2 = 36\), so \(2^6 > 6^2\)
2. \(4^3 = 64\) and \(2^6 = 64\), so \(4^3 = 2^6\)

Scoring: 1 point for each correct symbol, supported by the values.

Question 8: Noah's Mistake (2 points)

1. Exponent: \(2^2 = 4\). Multiply: \(3\times 4 = 12\). Add: \(5 + 12 = \) \(17\)
2. Noah added \(5 + 3 = 8\) first and then multiplied by \(2^2 = 4\), getting \(8\times 4 = 32\). He should have multiplied before adding.

Scoring: 1 point for the correct value; 1 point for explaining that he added before multiplying.

Question 9: Garden Soil (3 points)

1. Area: \(9^2 = 81\) square feet. Answer: \(9^2 = 81\text{ ft}^2\)
2. Cost: \(2\times 9^2 + 15 = 2\times 81 + 15 = 162 + 15 = \) \(\$177\)

Scoring: Part (a): 1 point. Part (b): 1 point for a correct expression and 1 point for the correct total.

See every chapter on the Grade 6 math page.