1. Indices The plural of index is indices Remember: a n = a x a x a x…x a n times is called the base is called the index “a”“a” “n”“n” Scientific notation Standard form/scientific notation is used to write very small or large numbers in index form. e.g. 100 = 1 x 10 x 10 4600000 = 0.00000713 = = 1 x 10 2 = 1.0 x 10 2 4.6 x 10 6 7.13 x 10 -6

2. Law of indices Rule 3: when you have one power to the power of another, you the numbers in the power: e.g. (x 2 ) 3 = (a 4 ) -2 = Rule 1: when you multiplying two expressions involving powers, you the numbers in the power: Rule 2: when you divide two expressions involving powers, you the numbers in the power: e.g. a 8 ÷ a 3 = m 10 ÷ m 8 = amanaman e.g. a 3 x a 4 = y -1 x y 6 = a m x a n = = a m - n (a m ) n = add a 3 + 4 = a 7 y -1+ 6 = y 5 a m+ n take away a 8 - 3 = a 5 m 10 - 8 = m 2 multiply a mn x 2 * 3 = x 6 a 4 * -2 = a - 8

3. Anything to the is equal to itself: Useful extras e.g. 5 1 = 17 1 = 35627658 1 = Anything to the power 0 is equal to 1: e.g. 5 0 =117 0 =135627658 0 = 1 i.ea 2 a x a 1 a 2 a x a 1 a 0 = = == 1 power 1 5 17 35627658 Anything to a involves dividing: e.g. 3 -2 = a -4 = 5x -2 = == 1am1am a 1 =a a 0 =1 a -m = negative power 1321913219 1a41a4 1 x 2 5 x 2 5 *

4. Fractional indices Any term with a fractional index of is the nth root e.g.= == Any term with a fractional index of is the nth root to the power m. e.g.=2m 2 x = = 4 Surd form Index form 23

5. Indices The plural of index is indices Remember: a n = a x a x a x…x a n times is called the base is called the index Scientific notation Standard form/scientific notation is used to write very small or large numbers in index form. e.g. 100 = 1 x 10 x 10 4600000 = 0.00000713 = = 1 x 10 2 = 1.0 x 10 2

6. Law of indices Rule 3: when you have one power to the power of another, you the numbers in the power: e.g. (x 2 ) 3 = (a 4 ) -2 = Rule 1: when you multiplying two expressions involving powers, you the numbers in the power: Rule 2: when you divide two expressions involving powers, you the numbers in the power: e.g. a 8 ÷ a 3 = m 10 ÷ m 8 = amanaman e.g. a 3 x a 4 = y -1 x y 6 = a m x a n = (a m ) n =

7. Anything to the is equal to itself: Useful extras e.g. 5 1 = 17 1 = 35627658 1 = Anything to the power 0 is equal to 1: e.g. 5 0 =117 0 =135627658 0 = 1 i.ea 2 a x a 1 a 2 a x a 1 a 0 = = == 1 Anything to a involves dividing: e.g. 3 -2 = a -4 = 5x -2 = == a 1 = a 0 = a -m =

8. Fractional indices Any term with a fractional index of is the nth root e.g.= == Any term with a fractional index of is the nth root to the power m. e.g.=2m 2 x = = Surd form Index form