This presentation shows some worked examples of finding powers of real numbers using the Laws of Indices.

1. LAWS OF INDICES
Worked Examples

2. Example 1
Determine the value of
 32 × 34
Recall: 𝒂𝒎 × 𝒂𝒏 = 𝒂𝒎+𝒏
32 × 34
= 32+4
= 36
= 3 × 3 × 3 × 3 × 3 × 3
= 729
 36 × 3−5 × 3−1
36 × 3−5 × 3−1
= 36−5−1
= 30
Recall: 𝒂𝟎
= 𝟏
Therefore,
36
× 3−5
× 3−1
= 30
= 1

3. Example 2
Determine the value of
 56 ÷ 54
Recall: 𝒂𝒎 ÷ 𝒂𝒏 = 𝒂𝒎−𝒏
56 ÷ 54
= 56−4
= 52
= 5 × 5
= 25

27
24
27
24
= 27−4
= 23
= 2 × 2 × 2
= 8

4. Example 3
Determine the value of
 52 3
Recall: 𝒂𝒎 𝒏 = 𝒂𝒎×𝒏
52 3
= 52×3
= 56
= 5 × 5 × 5 × 5 × 5 × 5
= 15625
 42 −2
= 42×−2
= 4−4
Recall: 𝒂−𝒎
=
𝟏
𝒂𝒎
Therefore:
𝟒𝟐 −𝟐
= 𝟒−𝟒 =
𝟏
𝟒𝟒
=
𝟏
𝟒 × 𝟒 × 𝟒 × 𝟒
=
𝟏
𝟐𝟓𝟔

5. Example 4
Determine the value of
 27
1
3 × 32
1
5
Recall: 𝑎
1
𝑛 = 𝑛
𝑎
27
1
3 × 32
1
5
=
3
27 ×
5
32
= 3 × 2
= 6
 125
2
3 × 81
3
4
Recall: 𝑎
𝑚
𝑛 =
𝑛
𝑎𝑚
125
2
3 × 81
3
4
=
3
1252 ×
4
813
= 25 × 27
= 675