The lesson
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.
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
Powers mean repeated multiplication - and PEMDAS sets the order.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Reversing the order named in the problem. Write the ratio in the same order the words give you.
Treating a part-to-part ratio like a part-to-whole fraction without checking what the whole is.
Key ideas from this lesson
- What an exponent means
- Order of operations (PEMDAS)
Video walkthroughs
Order of Operations
PEMDAS step by step so you always know what to do first.
Watch on YouTube
Intro to Exponents
Understand repeated multiplication and exponent notation.
Watch on YouTube
Evaluating Expressions with Exponents
Substitute values and evaluate numeric expressions with powers.
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)