The lesson
This lesson teaches Exponents & Order of Operations. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
What an exponent means
An exponent is a shortcut for repeated multiplication. 4³ means 4 × 4 × 4 = 64. The small number (the exponent) tells you how many times to multiply the base by itself.
When you study what an exponent means, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Order of operations (PEMDAS)
When an expression has several operations, do them in this order: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).
A ratio compares two quantities with the same units. Order matters: a ratio of cats to dogs is not the same as dogs to cats unless the problem says they are equivalent.
Write ratios in three ways: with a colon (3:4), as a phrase (3 to 4), or as a fraction (3/4) when it fits the context.
2 + 3 × (4² − 6)
- 1Parentheses first, and inside them exponents: 4² = 16.
- 216 − 6 = 10, so the expression is 2 + 3 × 10.
- 3Multiply: 3 × 10 = 30. Then add: 2 + 30 = 32.
Why this matters
Exponents & Order of Operations shows up constantly in powers mean repeated multiplication - and PEMDAS sets the order. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- What an exponent means
- Order of operations (PEMDAS)
Video walkthrough
Order of Operations
PEMDAS step by step so you always know what to do first.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfEvaluate: 5².
Step-by-step solution
- 15² means 5 × 5.
- 25 × 5 = 25.
Exercise 2
Try it yourselfEvaluate: 2 + 3² × 2.
Step-by-step solution
- 1Exponent first: 3² = 9.
- 2Multiply: 9 × 2 = 18.
- 3Add: 2 + 18 = 20.
Exercise 3
Try it yourselfEvaluate: (8 − 3)² ÷ 5.
Step-by-step solution
- 1Parentheses: 8 − 3 = 5.
- 2Exponent: 5² = 25.
- 3Divide: 25 ÷ 5 = 5.
Exercise 4
Try it yourselfEvaluate: 48 ÷ 6 × 2 + 1.
Step-by-step solution
- 148 ÷ 6 = 8.
- 28 × 2 = 16.
- 316 + 1 = 17.
Exercise 5
Try it yourselfEvaluate: 4 × (2 + 3)² − 10.
Step-by-step solution
- 1Parentheses: 2 + 3 = 5.
- 2Exponent: 5² = 25.
- 3Multiply: 4 × 25 = 100.
- 4Subtract: 100 − 10 = 90.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Exponents & Order of Operations
Question 1 of 5
Evaluate: 2 + 3 × (4² − 6)