Transcript INDICES

The Index is the power to which a
number is raised.
3³ ('3 cubed' or '3 to the power of
3') =3X3X3
5² ('5 squared' or 5 'to the power'
of 2)=5X5
are example of numbers in Index
Form.
Index
3⁴
Base
First Law of Indices:
Product
₅⁵x₅⁴
=(5X5X5X5X5)X(5X5X5X5)
=5⁹
=5⁽⁵⁺⁴⁾
First Law of Indices:
Product
When we multiply together index numbers, we add
the powers. So:
ya × yb = ya+b
Second Law of Indices:
Quotient
₅⁹
₅⁴
=
=
=
5x5x5x5x5x5x5x5x5
5x5x5x5
5x5x5x5x5
5⁵ = 5 ⁽⁹⁻⁴⁾
Second Law of Indices:
Quotient
Division
When dividing index numbers, we subtract the power
of the number we are dividing by from the power of
the number being divided. So:
ya ÷ yb = ya - b
Third Law of Indices: Power
(₅²)⁴ =
(5X5) X (5X5) X (5X5) X (5X5)
= 5⁸
= 5⁽⁴ x ²⁾
= 5⁸
Third Law of Indices: Power
(ym)ⁿ
=
y
=
m n 
The Zero Index
Anything to the power 0 is equal to 1.
So 30 = 1,
8240 = 1
and x0 = 1.