A PowerPoint Presentation I created to help explain the Index Laws

1. EXPONENT (POWER)
LAWS
If a is any number and m
any positive integer
(whole number) then
the product of a with
itself m times is called a
raised to the power m
and written
am

2. Product of
Powers
Property
E.g. 23 x 25 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
= 8 x 32
= 256
OR
by using the Product of Powers Property which
states that when Numbers with the same Base are
Multiplied, the Indices are Added
am x an = am + n
E.g. 23 + 5 = 28
= 256

3. Quotient of
Powers
Property
E.g.
𝟕 𝟓
𝟕 𝟑 =
7 ∙7 ∙7 ∙7 ∙7
7 ∙7 ∙7
7 ∙7∙7∙7 ∙7
7∙7∙7
= 7 x 7
= 49
OR
by using the Quotient of Powers Property which
states when Numbers with the same Base are
Divided, the Indices are Subtracted
𝒂 𝒎
𝒂 𝒏 = am - n
E.g. 75 - 3 = 72
= 49

4. Power of a
Power
Property
E.g. (54)3 = 54 x 54 x 54
= 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
= 512
OR
To remove Brackets, use the Power of a Power
Property by Multiplying the Index inside the
Brackets by the Index outside the Brackets
(am)n = am x n
E.g. 54 x 3 = 512

5. Power of a
Product
Property
E.g. (3 x 5)3 = (3 x 5)(3 x 5) (3 x 5)
= 3 x 5 x 3 x 5 x 3 x 5
= 3 3 5 3
OR
To remove Brackets containing a Product, use the
Power of a Product Property by raising every part of
the Product to the Index outside the Brackets.
(ab)m = am bm
E.g. (3 x 5)3 = 3353

6. Power of a
Quotient
Property
E.g.
𝟐
𝟕
𝟑 = (
2
7
) x (
2
7
) x (
2
7
)
=
2 ∙ 2 ∙ 2
7 ∙ 7 ∙ 7
=
23
73
OR
To remove Brackets containing a Fraction, use the
Power of a Quotient Property by Multiplying the Indices
of both Numerator and Denominator by the Index
outside the Brackets.
𝒂
𝒃
𝒎 =
𝒂 𝒎
𝒃 𝒎
E.g.
𝟐
𝟕
𝟑 =
23
73

7. Zero
Exponent
and
Negative
Exponent
The Zero Exponent states that any Term (excluding 0) with
an Index of 0 is equal to
a 𝟎 = 𝟏
The Negative Exponent states that a Power with a
Negative Exponent equals 1 Divided by that Power with its
Opposite Exponent
a-n =
𝟏
𝒂 𝒏