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.
What you'll learn
- Evaluate expressions with exponents
- Apply order of operations
- Use parentheses to control grouping
Why it matters: Compound interest, computer memory (kilobyte, megabyte, gigabyte), and scientific units all use exponents. Order of operations is the rule that keeps everyone's calculator answer matching.
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.
Answer: 35
Practice problems
1. Evaluate 4^2.
Show solution
- Warm-up: First identify exactly what the question is asking: Evaluate 4^2.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 4^2 means 4 x 4.
- 4 x 4 = 16.
- Check the result by substituting or estimating: the response should match 16 and make sense in the original problem.
Answer: 16
2. Evaluate 2^5.
Show solution
- Warm-up: First identify exactly what the question is asking: Evaluate 2^5.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 2^5 means five factors of 2.
- 2 x 2 x 2 x 2 x 2 = 32.
- Check the result by substituting or estimating: the response should match 32 and make sense in the original problem.
Answer: 32
3. Evaluate 9 - 3 x 2.
Show solution
- Warm-up: First identify exactly what the question is asking: Evaluate 9 - 3 x 2.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Multiply before subtracting.
- 3 x 2 = 6, then 9 - 6 = 3.
- Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.
Answer: 3
4. Evaluate (9 - 3) x 2.
Show solution
- Core Practice: First identify exactly what the question is asking: Evaluate (9 - 3) x 2.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Parentheses first: 9 - 3 = 6.
- Then 6 x 2 = 12.
- Check the result by substituting or estimating: the response should match 12 and make sense in the original problem.
Answer: 12
5. Evaluate 6 + 4^2.
Show solution
- Core Practice: First identify exactly what the question is asking: Evaluate 6 + 4^2.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Exponent first: 4^2 = 16.
- 6 + 16 = 22.
- Check the result by substituting or estimating: the response should match 22 and make sense in the original problem.
Answer: 22
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