Exponents and Order of Operations
A free Pre-Algebra lesson from the “Algebra Readiness” unit, with a worked example and practice problems including step-by-step solutions.
Order of operations keeps expressions consistent: parentheses first, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. In Algebra Readiness, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Evaluate expressions with exponents
- Apply order of operations
- Use parentheses to control grouping
Worked example
Problem. Evaluate 3 + 2^3 x 4.
- Evaluate the exponent first: 2^3 = 8.
- Multiply next: 8 x 4 = 32.
- Add last: 3 + 32 = 35.
- Connect the calculation back to Exponents and Order of Operations so the method, not just the arithmetic, is clear.
Answer: 35
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Evaluate 4^2.
Show solution
- 4^2 means 4 x 4.
- 4 x 4 = 16.
Answer: 16
2. Evaluate 2^5.
Show solution
- 2^5 means five factors of 2.
- 2 x 2 x 2 x 2 x 2 = 32.
Answer: 32
3. Evaluate 9 - 3 x 2.
Show solution
- Multiply before subtracting.
- 3 x 2 = 6, then 9 - 6 = 3.
Answer: 3
4. Evaluate (9 - 3) x 2.
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- Parentheses first: 9 - 3 = 6.
- Then 6 x 2 = 12.
Answer: 12
5. Evaluate 6 + 4^2.
Show solution
- Exponent first: 4^2 = 16.
- 6 + 16 = 22.
Answer: 22
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