6th Grade Exponents and Order of Operations Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Exponents and Order of Operations – Maths PDF

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This exponents practice solutions for 6th Grade covers exponents and order of operations (Common Core 6.EE.A.1, 6.EE.A.2c), with a free PDF to print.

Check your work here. Each solution evaluates powers first, shows each operation in order, and gives a final answer in bold. Figures illustrate squares, cubes, and tables of powers.

Grade 6 · Common Core State Standards: 6.EE.A.1, 6.EE.A.2c

Exponents practice solutions: exercises 1 to 10

Exercise 1 – Write as a power

The factor 5 is used 4 times.

\(5^{4}\); base 5, exponent 4

Exercise 2 – Expand a power

\(2^{5} = 2 \times 2 \times 2 \times 2 \times 2\)

\(2 \times 2 = 4\), \(4 \times 2 = 8\), \(8 \times 2 = 16\), \(16 \times 2 = 32\).

\(32\)

Exercise 3 – Square arrangement

Area = side times side = \(3 \times 3 = 3^{2}\).

\(3^{2} = 9\) square units

Nine unit squares: 3 squared is 9.

Exercise 4 – Evaluate a power

\(3^{4} = 3 \times 3 \times 3 \times 3 = 9 \times 9 = 81\)

Exercise 5 – Powers of ten

The exponent tells how many zeros follow the 1.

\(10^{3} = 1{,}000\) and \(10^{6} = 1{,}000{,}000\).

1,000 and 1,000,000

Exercise 6 – Power plus a number

Evaluate the power first: \(4^{2} = 16\).

\(16 + 3 = 19\)

Exercise 7 – Fraction base

\(\left(\frac{1}{2}\right)^{3} = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}\)

\(\frac{1}{8}\)

Exercise 8 – Decimal base

\(0.5 \times 0.5 = 0.25\)

\(0.25\)

Exercise 9 – Multiplication before subtraction

Multiply first: \(2 \times 5 = 10\).

\(18 – 10 = 8\)

Exercise 10 – Division, addition, and exponent

Exponent: \(3^{2} = 9\). Division: \(24 \div 4 = 6\).

\(6 + 9 = 15\)

Exercises 11 and up

Exercise 11 – Parentheses

Parentheses first: \(8 – 3 = 5\).

Multiply: \(2 \times 5 = 10\). Add: \(5 + 10 = 15\).

Exercise 12 – Exponent before multiplication

\(4^{2} = 16\). \(3 \times 16 = 48\). \(48 – 10 = 38\).

Exercise 13 – Grouping with an exponent

Parentheses: \(6 + 4 = 10\). Exponent: \(10^{2} = 100\).

\(100 \div 5 = 20\)

Exercise 14 – Substitute a value

Replace x with 4: \(3 \times 4 + 5\).

\(12 + 5 = 17\)

Exercise 15 – Substitute into a power

\(6^{2} – 3 = 36 – 3 = 33\)

Exercise 16 – Two variables

\(2(3 + 5) = 2 \times 8 = 16\)

Exercise 17 – Volume of a cube

\(V = 4^{3} = 4 \times 4 \times 4\)

\(4 \times 4 = 16\), \(16 \times 4 = 64\).

\(64\text{ in}^{3}\)

Exercise 18 – Perimeter formula

\(P = 2 \times 12 + 2 \times 7 = 24 + 14 = 38\)

\(38\text{ ft}\)

Exercise 19 – Area of a square

\(2.5^{2} = 2.5 \times 2.5 = 6.25\)

\(6.25\text{ m}^{2}\)

Exercise 20 – Doubling bacteria

\(2^{6} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64\)

64 bacteria

Each hour is twice the last: 2^6 = 64.

Exercise 21 – Garden plan

\((6 + 2)^{2} – 6^{2}\)

\(8^{2} = 64\) and \(6^{2} = 36\).

\(64 – 36 = 28\)

\(28\text{ ft}^{2}\)

The big square is 64 square feet and the garden is 36, so the path is 28 square feet.

Key facts behind this exponents practice solutions

Key facts

In b^n, the base b is used as a factor n times.
Squares and cubes: 3^2 = 9 and 2^3 = 8.
Order of operations: parentheses, exponents, multiply or divide, add or subtract.
Powers of 10 have as many zeros as the exponent.
To evaluate an expression with a variable, substitute then follow the order of operations.

How to use this exponents practice solutions

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

All Grade 6 chapters: Grade 6 math.

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