Powers and order of operations
Read an exponent as repeated multiplication and evaluate expressions in a consistent order.
Before you begin
- Multiplication and division
- Grouping with brackets
Read the base and exponent
In 4³, the base 4 is the repeated factor and the exponent 3 counts how many factors are multiplied: 4 × 4 × 4 = 64. It does not mean 4 × 3. Squaring a side length produces an area; cubing it produces a volume. Write out a short power as a product when checking a calculation or explaining why two powers are different.
Respect the structure of an expression
Evaluate grouping symbols first, then powers, then multiplication and division from left to right, then addition and subtraction from left to right. Multiplication does not automatically come before division when they appear at the same level. Brackets can change the result because they make a group act as a single quantity. Show intermediate lines so the order of your calculation is visible.
Worked example
Evaluate 3 + 2 × (5² − 16).
Show the worked solution
- Calculate inside the brackets: 5² = 25, and 25 − 16 = 9.
- Multiply before adding: 2 × 9 = 18.
- Add the remaining 3 to obtain 21.
21.
Try it yourself
What is 24 ÷ 6 × 2?
Common mistakes
- An exponent counts repeated factors, not a multiplier.
- Operations with equal priority are handled from left to right.
What can you explain now?
Evaluate 5² − 3 × 4 + 2 and compare it with (5² − 3) × 4 + 2.
Compare with the explanation
15 and 90.
The first is 25 − 12 + 2 = 15. In the second, the bracket gives 22 before multiplication, so 22 × 4 + 2 = 90.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗