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

Problem 1: Writing Products as Powers

1. Three factors of 5: \(5^3\). Answer: \(5^3\)
2. Five factors of 7: \(7^5\)
3. Two factors of 9: \(9^2\)
4. Six factors of 2: \(2^6\)

Problem 2: Evaluating Powers

1. \(3^4 = 3\times 3\times 3\times 3 = 9\times 9 = \) \(81\)
2. \(2^6 = 4\times 4\times 4 = 16\times 4 = \) \(64\)
3. \(5^3 = 25\times 5 = \) \(125\)
4. \(8^2 = 8\times 8 = \) \(64\)

Problem 3: Powers of 10

1. \(100,000\) has five zeros after the 1: \(10^5\)
2. \(10,000,000\) has seven zeros: \(10^7\)
3. \(10^4\) is a 1 followed by four zeros: 10,000
4. \(10^6\) is a 1 followed by six zeros: 1,000,000

Problem 4: Order of Operations Without Exponents

1. Multiply first: \(4\times 3 = 12\). Then \(5 + 12 = \) \(17\)
2. Multiply first: \(4\times 5 = 20\). Then \(30 – 20 = \) \(10\)
3. Left to right: \(24: 4 = 6\), then \(6\times 3 = \) \(18\)
4. Divide first: \(6: 3 = 2\). Then \(18 – 2 + 2 = 16 + 2 = \) \(18\)

Problem 5: Grouping Symbols

1. Parentheses: \(9+3 = 12\). Then \(12\times 2 = \) \(24\)
2. Parentheses: \(2+3 = 5\). Then \(40: 5 = \) \(8\)
3. Parentheses: \(12-7 = 5\). Then \(5\times 5 = \) \(25\)
4. Parentheses: \(3\times 2 = 6\). Then \(36: 6 = 6\) and \(6 + 1 = \) \(7\)

Problem 6: Exponents in Expressions

1. Exponent first: \(3^2 = 9\). Then \(2\times 9 = \) \(18\)
2. Parentheses: \(2\times 3 = 6\). Then \(6^2 = \) \(36\)
3. Exponent first: \(4^2 = 16\). Then \(50 – 16 = \) \(34\)
4. Exponents: \(5^2 = 25\) and \(3^3 = 27\). Then \(25 + 27 = \) \(52\)

Problem 7: Mixed Expressions

1. \(2^3 = 8\). Then \(8\times 4 = 32\). Then \(6 + 32 – 10 = 38 – 10 = \) \(28\)
2. \(5^2 = 25\). Then \(100: 25 = 4\). Then \(4 + 7 = \) \(11\)
3. Parentheses: \(4+2 = 6\). Exponent: \(6^2 = 36\). Then \(3\times 36 = \) \(108\)
4. Exponent: \(2^2 = 4\). Parentheses: \(20 – 4 = 16\). Then \(16: 4 = \) \(4\)

Problem 8: Finding an Error

Maya added \(3 + 2 = 5\) first and then computed \(5\times 5^2 = 5\times 25 = 125\). Exponents and multiplication come before addition.

Exponent: \(5^2 = 25\). Multiplication: \(2\times 25 = 50\). Addition: \(3 + 50 = 53\). Correct value: \(53\)

Problem 9: Patio Cost

The area is \(8^2\) square feet, and paving costs $3 per square foot, so the paving costs \(3\times 8^2\). Add the $10 delivery fee: \(3\times 8^2 + 10\).

Exponent: \(8^2 = 64\). Multiply: \(3\times 64 = 192\). Add: \(192 + 10 = 202\).

Total cost: \(\$202\)

Problem 10: Chain Message

1. Day 4: \(3^4 = 3\times 3\times 3\times 3 = 81\). Answer: \(3^4 = 81\) people
2. Day 5: \(3^5 = 81\times 3 = 243\). Answer: 243 people
3. \(3^5 – 3^4 = 243 – 81 = 162\). Answer: 162 more people

See every chapter on the Grade 6 math page.