Practice Operation Hierarchy in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The layered relationship between arithmetic operations, where each is built from the previous: multiplication from addition, exponentiation from multiplication.

Multiplication is repeated addition. Exponents are repeated multiplication.

Showing a random 20 of 50 problems.

Example 1

easy

Evaluate

10 - 2 \times 3 + 1

Example 2

hard

Evaluate

\dfrac{2^4 - 2 \times 3}{5}

Example 3

hard

Evaluate

-3^2 + (-3)^2

Example 4

challenge

Evaluate

2 + 3 \times (4 - 1)^2

Example 5

medium

Evaluate

6 + 2 \times 5 - 4 \div 2

Example 6

easy

2^3

equal to

2 \times 3

? (yes/no)

Example 7

medium

Evaluate

\dfrac{4^2 - 1}{5}

Example 8

hard

Evaluate

\sqrt{16} + 3 \times 2^2 - 6 \div 3

Example 9

easy

8 - 6 \div 2

, which operation comes first?

Example 10

medium

Evaluate

2 + 3 \times 4^2

Example 11

medium

Evaluate

2 + 3^2 \times (4 - 1) \div 9

Example 12

medium

Evaluate

48 \div 2 \div 4

Example 13

easy

Evaluate

9 - 2^2

Example 14

medium

Evaluate

36 \div 6 + 2 \times 3

Example 15

easy

Which operation is at the top of the hierarchy: addition, multiplication, or exponentiation?

Example 16

medium

Evaluate

2^3 + 2^2

Example 17

easy

Evaluate

12 \div 4 + 3

Example 18

medium

Evaluate

(2 + 3) \times 4^2

Example 19

easy

Rewrite

2^3

as repeated multiplication.

Example 20

medium

Evaluate

50 - 3^2 \times 2

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Related Concepts

Addition Multiplication Exponents