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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

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.

  1. Evaluate the exponent first: 2^3 = 8.
  2. Multiply next: 8 x 4 = 32.
  3. Add last: 3 + 32 = 35.
  4. Connect the calculation back to Exponents and Order of Operations so the method, not just the arithmetic, is clear.

Answer: 35

Practice problems

1. Evaluate 4^2.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Evaluate 4^2.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 4^2 means 4 x 4.
  4. 4 x 4 = 16.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Evaluate 2^5.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 2^5 means five factors of 2.
  4. 2 x 2 x 2 x 2 x 2 = 32.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Evaluate 9 - 3 x 2.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Multiply before subtracting.
  4. 3 x 2 = 6, then 9 - 6 = 3.
  5. 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
  1. Core Practice: First identify exactly what the question is asking: Evaluate (9 - 3) x 2.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Parentheses first: 9 - 3 = 6.
  4. Then 6 x 2 = 12.
  5. 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
  1. Core Practice: First identify exactly what the question is asking: Evaluate 6 + 4^2.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Exponent first: 4^2 = 16.
  4. 6 + 16 = 22.
  5. 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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