5^{2} 
In the example shown in the box, the 5 is called the base. The 2 is called the index or power or exponent. 5 to the power of 2 = 5 × 5 = 25
INDEX RULES  
Rules  Examples  
Expanding  a^{n} = a × a × a × ...... × a  3^{5} = 3 × 3 × 3 × 3 × 3 = 243  
Multiplying  a^{x} × a^{y} = a^{(x+y)}  3^{6} × 3^{2} = 3^{(6+2)} = 3^{8} = 6561  
Dividing  a^{x} ÷ a^{y} = a^{(x–y)}  3^{6} ÷ 3^{2} = 3^{(6–2)} = 3^{4} = 81  
Fractional index  a^{(1/x)} = x^{th} root of a  9^{(1/2)} = √9 = 3  
Negative index 


Expand 5^{3}
Answer:
5^{3}
= 5 × 5 × 5
= 125
The world's largest pillow fight flash mob occurred simultaneously on March 22nd, 2008 in 25 cities around the world. In New York City alone, it is estimated that 4000 people enjoyed the experience. Online communication via Facebook and email was used to organize the event.
If each person told exactly 2 people, and each of those 2 people told 2 more people and so forth, what is the approximate number of communications that could contact 4000 people?
Answer:
2 to the power of ? = 4000
2^{12} = 4096
(or 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 4096)
There would be approximately 12 communications to create this flash mob.
About every 20 minutes, bacteria reproduce by binary fission, similar to splitting in half. If there was 1 bacterium in a petri dish at the start of an experiment, how many would there be after 2 hours?
Answer:
No. of "splits"
= 2 hours ÷ 20 minutes
= 6 "splits"
No. of bacteria after 2 hours
= 2^{6}
= 64 bacteria
Expand these.
Q1. 5^{5}
Q2. 10^{6}
Answers
A1. 3125
A2. 1 000 000
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!
Calculate 2^{3} × 2^{6}. Leave the answer in index form.
Answer:
2^{3} × 2^{6}
= 2^{3+6}
= 2^{9}
Calculate 2^{3} × 5^{2} × 2^{4}. Leave the answer in index form.
Answer:
2^{3} × 2^{4} × 5^{2}
= 2^{3+4} × 5^{2}
= 2^{7} × 5^{2}
Multiply these indices. Leave the answer in index form.
Q1. 3^{2} × 3^{5}
Q2. 4^{3} × 4^{6}
Answers
A1. 3^{7}
A2. 4^{9}
Computer bytes do not use decimal numbers (base10 numbers). They use binary numbers (base2 numbers). Because computers use binary numbers, a "kilobyte" is not really a thousand bytes, but is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 or 1,024 bytes. Also, a "megabyte" is not a million bytes, but is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 or 1,048,576 bytes. Write a kilobyte and a megabyte using indices of base 2.
Calculate 2^{7} ÷ 2^{4}. Leave the answer in index form.
Answer:
2^{7} ÷ 2^{4}
=  2 × 2 × 2 × 2 × 2 × 2 × 2 
2 × 2 × 2 × 2 
= 2 × 2 × 2
= 2^{3}
Calculate 10^{5} ÷ 10^{3}. Leave the answer in index form.
Answer:
10^{5} ÷ 10^{3}
=  10 × 10 × 10 × 10 × 10 
10 × 10 × 10 
= 10 × 10
= 10^{2}
Divide these indices. Leave the answer in index form.
Q1. 3^{6} ÷ 3^{2}
Q2. 10^{5} ÷ 10^{2}
Answers
A1. 3^{4}
A2. 10^{3}
Calculate 100^{1/2}
Answer:
100^{(1/2)}
= √100
= 10
Calculate 27^{1/3}
Answer:
27^{(1/3)}
= ^{3}√27
= 3
Calculate these.
Q1. 64^{1/2}
Q2. 343^{1/3}
Answers
A1. 8
A2. 7
Calculate 5 ^{–2}
Answer:
5 ^{–2}
= 1 ÷ 5^{2}
= 1 ÷ 25
= ^{1}⁄_{25}
Calculate 10^{2} × 10 ^{–4}
Answer:
10^{2} × 10 ^{–4}
= 10^{2} × (1 ÷ 10^{4})
= 100 ÷ 10000
= ^{1}⁄_{100}
Calculate these.
Q1. 5 ^{–3}
Q2. 4 ^{–3} × 4 ^{–2}
Answers
A1. ^{1}⁄_{125}
A2. ^{1}⁄_{1024}
There are 10 kinds of people  those who can understand BINARY and those who can't!