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Exponents
Curator: K.L Morweng

Daily applications
 Imagine folding a paper
once, then twice, the thrice
etc. How many subsections
of that paper would you get?
 Imagine winning the Lottery
worth that many zeros.
 Evolution of space storage
i.e Memory cards, Hard
drives etc.
1MB= 1 x 106 bytes
1GB= 1 x 109 bytes

Mathematical definition of exponents
 An “abbreviation” or shortened form of
representing or expressing a very large
number or a very small number.
 a quantity representing the power to which a
given number or expression is to be raised,
usually expressed as a raised symbol beside
the number or expression.
 The exponent of a number says how many
times to use that number in a multiplication.

Exponential Notation
 Exponential notation refers to repeated multiplication
 Exponential notation is usually very useful when the same
number is repeatedly multiplied.
9 x 9 = 92
1 x 1 x 1 x 1 x 1 x 1= 16
 The number being repeatedly multiplied is the base and the
exponent tells us how many times our base has been multiplied.
Exponent
Base

Special case 1
“Squared” exponents
 The number with the exponent 2 is referred to as the “square” of
that number
52 Five squared.
 The square can be used in other dimensions such as measuring the
Area of a shape.
 E.g. Calculate the area of a square whose side is 5m.
A = side x side
= 5m x 5m
= 25m2 (25 meters squared)

Special case 2
“Cubed” exponents
 A number with an exponent of three (3) is referred to as a “cube” of
the base.
53 Five cubed
 The cube can be used in other dimensions such as measuring the
Volume of a shape.
 E.g. Calculate the volume of a square whose side is 5m.
V = side x side x side
= 5m x 5m x 5m
= 125m2 (125 meters cubed)
 The square and cube of a whole number is referred to as a
“perfect square”

Rules
The invisible exponent
 When a number or expression does not have a
visible exponent, the exponent is 1.
1
xx 

Exponent rule #1 (Product rule)
 When multiplying two numbers or expressions with the
same base, we ADD their exponents.
 For example
mn
b 
 42
xx 42
x 6
x
 2
22 21
22  21
2 
 3
2 8

Exponent rule #2 (Quotient rule)
 When dividing two expressions with the same base you
subtract their exponents.
 For example
m
n
a
a mn
a
-
2
5
x
x -25
x
3
x

Continue…
 Try it on your own:
m
n
a
a mn
a
-
2
6
h
h
-26
h 4
h

3
33
-13
3 2
3 9

Exponent rule #3 (Power rule)
 When raising a power to a power you multiply the exponents
 For example:
32
)2( 32
2

 6
2 64
mn
b )( mn
b 

42
)(x 42
 x 8
x

Continue…
 Try it on your own
23
)(k 23
 k
6
k
22
)3(
mn
b )( mn
b


22
3

 4
3 81

Note!!!
 When using this rule the exponent can not
be brought in the parenthesis if there is
addition or subtraction

You would have to use FOIL in these cases
44
2x222
)2( x

Exponent rule #4
 When a product is raised to a power, each piece is raised to the
power
 Example:
m
ab)( mm
ba
2
)(xy 22
yx
2
)52(  22
52  254 100

Continued…
 Try it on your own:
3
)(hk
2
)32( 
m
ab)( mm
ba
33
kh
22
32  94 36

Note!!!
 This rule is for products only. When using
this rule the exponent can not be brought in
the parenthesis if there is addition or
subtraction
You would have to use FOIL in these cases
2
)2( x  22
2x

Exponent Rule #5






m
b
a
m
m
b
a






2
.9
k
h
2
2
k
h






2
2
4
.10 2
2
2
4
4
16
 4

Zero Exponent
 When anything, except 0, is raised to the zero power it is 1.
 For example
0
a 1 ( if a ≠ 0)
0
x 1 ( if x ≠ 0)
0
25 1

Zero Exponent
0
a 1 ( if a ≠ 0)
0
.11 h 1( if h ≠ 0)
1
0
0.13 undefined
0
100.12

Negative Exponents
 If b ≠ 0, then
 For example:
-n
b n
b
1
-2
x 2
1
x
-2
3 2
3
1
9
1


Sources:
Heywood, R (2009) Exponent Power Point . Available from �ݺ�ߣshare at
/rheywood/exponent-power-point (Accessed 14 September 2017)
Makhanda, O (2014) Basics about exponents. Available from �ݺ�ߣshare at
/oneill0205/basics-about-exponents?qid=8e51a4ad-4d2c-4ca1-8dc6-
010590bf2d12&v=&b=&from_search=1 (Accessed 13 September 2017).
McDonald (2010) Exponents in Real Life. Available from �ݺ�ߣshare at
/MrMacD/exponents-in-real-life (Accessed 14 September 2017)
Phillips, G (2012) Exponent rules. Available from �ݺ�ߣshare at
/genny_simpson/exponent-rules-12027519?qid=3e09689b-a929-4627-
8c79-83a659b0bc82&v=&b=&from_search=2 (Accessed 10 September 2017).
Watt, R (2009) Nov. 19 More Exponent Rules. . Available from �ݺ�ߣshare at
/RyanWatt/nov-19-more-exponent-rules?qid=fb261152-c0b7-4b96-
8eb2-c4fecb740b20&v=&b=&from_search=1 (Accessed 10 September 2017).

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Exponent properties

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