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

Problem 1: Writing Products as Powers

Write each product using an exponent.

1. \(5\times 5\times 5\)
2. \(7\times 7\times 7\times 7\times 7\)
3. \(9\times 9\)
4. \(2\times 2\times 2\times 2\times 2\times 2\)

Problem 2: Evaluating Powers

Evaluate each power.

1. \(3^4\)
2. \(2^6\)
3. \(5^3\)
4. \(8^2\)

Problem 3: Powers of 10

Write each number as a power of 10 or in standard form.

1. \(100,000\)
2. \(10,000,000\)
3. \(10^4\)
4. \(10^6\)

Problem 4: Order of Operations Without Exponents

Evaluate each expression.

1. \(5 + 4\times 3\)
2. \(30 – 4\times 5\)
3. \(24: 4\times 3\)
4. \(18 – 6: 3 + 2\)

Problem 5: Grouping Symbols

Evaluate each expression.

1. \((9+3)\times 2\)
2. \(40: (2+3)\)
3. \(5\times (12-7)\)
4. \(36: (3\times 2) + 1\)

Problem 6: Exponents in Expressions

Evaluate each expression.

1. \(2\times 3^2\)
2. \((2\times 3)^2\)
3. \(50 – 4^2\)
4. \(5^2 + 3^3\)

Problem 7: Mixed Expressions

Evaluate each expression.

1. \(6 + 2^3\times 4 – 10\)
2. \(100: 5^2 + 7\)
3. \(3\times (4+2)^2\)
4. \((20 – 2^2): 4\)

Problem 8: Finding an Error

Maya evaluated \(3 + 2\times 5^2\) and got \(125\). Explain her error and find the correct value.

Problem 9: Patio Cost

A square patio has sides of \(8\text{ ft}\). Paving costs $3 per square foot, and delivery costs a flat $10. Write one expression with an exponent for the total cost, then evaluate it.

Problem 10: Chain Message

Mei starts a chain message. On day 1, \(3\) classmates receive it. Each day after that, every new receiver sends it to \(3\) people who have not seen it, so the number of new receivers on day \(n\) is \(3^n\).

1. Write the number of new receivers on day 4 as a power and evaluate it.
2. Find the number of new receivers on day 5.
3. Write and evaluate an expression for how many more people receive the message on day 5 than on day 4.

See every chapter on the Grade 6 math page.