Exponent Rules

52

In the example shown in the box, the 5 is called the base. The 2 is called the exponent or index or power. 5 to the power of 2 = 5 × 5 = 25


INDEX RULES
RulesExamples
Expandingan = a × a × a × ...... × a35 = 3 × 3 × 3 × 3 × 3 = 243
Multiplyingax × ay = a(x+y)36 × 32 = 3(6+2) = 38 = 6561
Dividingax ÷ ay = a(x–y)36 ÷ 32 = 3(6–2) = 34 = 81
Fractional indexa(1/x) = xth root of a9(1/2) = √9 = 3
Negative index
a –1 = 1
ax
3 –2 = 1 = 1
329


Example One - Expanding

Expand 53

Answer:
53
= 5 × 5 × 5
= 125

Questions

Expand these.
Q1. 55
Q2. 106

Answers
A1. 3125
A2. 1 000 000

Maths Fun - Body Bacteria

How many bacteria are on your body NOW? Here are some facts to help you work it out...

That probably took a minute for you to work out. How many bacteria are on your skin NOW (a minute later)? Bacteria reproduce by binary fission (splitting in half) every 20 minutes. Therefore, all those bacteria have reproduced (doubled in number) 3 times in the last minute!

Example Two - Multiplying Indices

Calculate 23 × 26. Leave the answer in index form.

Answer:
23 × 26
= 23+6
= 29


Example Three - Multiplying Indices

Calculate 23 × 52 × 24. Leave the answer in index form.

Answer:
23 × 24 × 52
= 23+4 × 52
= 27 × 52

Questions

Multiply these indices. Leave the answer in index form.
Q1. 32 × 35
Q2. 43 × 46

Answers
A1. 37
A2. 49

Example Four - Dividing Indices

Calculate 27 ÷ 24. Leave the answer in index form.

Answer:
27 ÷ 24

= 2 × 2 × 2 × 2 × 2 × 2 × 2
2 × 2 × 2 × 2

= 2 × 2 × 2

= 23


Example Five - Dividing Indices

Calculate 105 ÷ 103. Leave the answer in index form.

Answer:
105 ÷ 103

= 10 × 10 × 10 × 10 × 10
10 × 10 × 10

= 10 × 10

= 102

Questions

Divide these indices. Leave the answer in index form.
Q1. 36 ÷ 32
Q2. 105 ÷ 102

Answers
A1. 34
A2. 103

Example Six - Fractional Indices

Calculate 1001/2

Answer:
100(1/2)
= √100
= 10


Example Seven - Fractional Indices

Calculate 271/3

Answer:
27(1/3)
= 327
= 3

Questions

Calculate these.
Q1. 641/2
Q2. 3431/3

Answers
A1. 8
A2. 7

Example Eight - Negative Indices

Calculate 5 –2

Answer:
5 –2
= 1 ÷ 52
= 1 ÷ 25
= 125


Example Nine - Negative Indices

Calculate 102 × 10 –4

Answer:
102 × 10 –4
= 102 × (1 ÷ 104)
= 100 ÷ 10000
= 1100

Questions

Calculate these.
Q1. 5 –3
Q2. 4 –3 × 4 –2

Answers
A1. 1125
A2. 11024