Exponent notation review | Year 8

01 / LEARN

The idea, step by step

Count the equal factors

In $3^{4}$ , the base is 3 and the exponent is 4. It means $3 \times 3 \times 3 \times 3$ , not $3 \times 4$ . The exponent counts equal factors. A square has exponent 2; a cube has exponent 3. Raising a number to the first power gives that number.

Brackets define the base

In ${(- 2)}^{4}$ , the whole bracketed number -2 is the base. Four negative factors give a positive result. In $- 2^{4}$ , the exponent applies to 2 first, then the outside minus sign is applied. Expanding the product is a useful way to check signs before using shortcuts.

A common trap

$5^{3}$ means $5 \times 3$ .

Instead: It means three factors of 5: $5 \times 5 \times 5 = 125$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

A positive base

Evaluate $3^{4}$ .

$3^{4} = 3 \times 3 \times 3 \times 3$ .
$9 \times 9 = 81$ .

Example 2

Compare the brackets

Evaluate ${(- 2)}^{4}$ and $- 2^{4}$ .

${(- 2)}^{4} = (- 2) (- 2) (- 2) (- 2) = 16$ .
$- 2^{4} = - (2 \times 2 \times 2 \times 2) = - 16$ .

16 and -16 respectively.

Check your understanding

Write $4 \times 4 \times 4 \times 4 \times 4$ as a power.

Show answer

$4^{5}$

The base 4 occurs five times.

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Evaluate $2^{5}$ .
2 marks
Evaluate $5^{3}$ .
2 marks
Evaluate ${(- 3)}^{2}$ .
2 marks
Evaluate $- 3^{2}$ .
2 marks
Write $7 \times 7 \times 7$ as a power.
1 mark
Which is larger: $2^{6}$ or $6^{2}$ ? Show both values.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Evaluate $2^{5}$ .
2 marks
$2 \times 2 \times 2 \times 2 \times 2 = 32$ .
32
Evaluate $5^{3}$ .
2 marks
$5 \times 5 \times 5 = 125$ .
125
Evaluate ${(- 3)}^{2}$ .
2 marks
$(- 3) (- 3) = 9$ .
9
Evaluate $- 3^{2}$ .
2 marks
$- (3 \times 3) = - 9$ .
-9
Write $7 \times 7 \times 7$ as a power.
1 mark
There are three equal factors of 7.
$7^{3}$
Which is larger: $2^{6}$ or $6^{2}$ ? Show both values.
3 marks
$2^{6} = 64$ and $6^{2} = 36$ .
$2^{6} = 64$ is larger than $6^{2} = 36$ .

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Exponent notation review; multiplying same-base powers; dividing same-base powers; powers of powers; zero index; combining numerical index laws. Negative indices and general variable index laws become Year 9 core.

Official curriculum source ↗

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