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Exponents and Order of Operations

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Exponents and Order of Operations

Evaluate expressions by working through grouping, exponents, multiplication or division, then addition or subtraction. Show your working where space is provided.

Understanding Exponents

1.Which repeated multiplication is represented by 6³?

6 × 3
6 × 6 × 6
3 × 3 × 3 × 3 × 3 × 3
6 + 6 + 6

2.Evaluate 3⁴. Write it first as repeated multiplication.

3.Which expression has a value of 216?

6³
6²
3⁴
2⁶

4.Complete the sequence of powers: 4¹ = 4, 4² = 16, 4³ = , 4⁴ = .

Order of Operations

Use the order: grouping, exponents, multiplication or division from left to right, then addition or subtraction from left to right.

5.Evaluate 5² + 3 × 4.

6.Calculate (7 − 2)² + 6.

7.Work out 4 × 2³ + 18 ÷ 3.

8.In 9 + 3² × 2, which operation should be completed first?

Add 9 and 3
Evaluate 3²
Multiply 3 by 2
Add 9 and 2

Using Exponents in Context

9.A square courtyard has sides 6 metres long. What is its area? Then find the combined area of 4 identical courtyards.

10.A woven design is made from 3 equal layers, each containing 4² small squares, plus 7 extra squares. Write an expression and calculate the total number of squares.

11.Give one reason why following the order of operations matters when evaluating a numerical expression.