1. INDICES

2. 3³ ('3 cubed' or '3 to the power of 3') =3X3X3
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.

3. Index
3 ⁴
Base

4. First Law of Indices: Product
₅⁵x₅⁴
=(5X5X5X5X5)X(5X5X5X5)
=5⁹
=5⁽⁵⁺⁴⁾

5. First Law of Indices: Product
When we multiply together index numbers, we add the powers. So: ya × yb = ya+b

6. Second Law of Indices: Quotient₅⁹ ₅⁴
= 5x5x5x5x5x5x5x5x5 5x5x5x5 = 5x5x5x5x5 = 5⁵ = 5 ⁽⁹⁻⁴⁾

7. 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

8. Third Law of Indices: Power
(₅²)⁴ = (5X5) X (5X5) X (5X5) X (5X5) = 5⁸ = 5⁽⁴ x ²⁾

9. Third Law of Indices: Power
(ym)ⁿ =

10. The Zero Index
Anything to the power 0 is equal to 1. So 30 = 1, 8240 = 1 and x0 = 1.