INDICES

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.

Index 3 ⁴ 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⁾

Third Law of Indices: Power (ym)ⁿ =

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