Multiplication in Algebra Involving Indices Title Multiplication Involving

Multiplication in Algebra Involving Indices

Title: Multiplication Involving Indices Objectives 1. Remember how to work out the HCF and LCM from any given pair of numbers 2. To understand how indices (powers) work in Algebra 3. To manipulate the powers in an expression in order to simplify it Anne Gilleran

Questions – simple multiplication 1) 7 ab x 8 pq 56 abpq 2) 3 f x 2 h x 5 a 30 afh 3) 3 abc x 4 def 12 abcdef 4) 5 g x 25 125 g 5) 5 mn x 2 pq x 4 40 mnpq 6) 5 f x g x h x 2 j 10 fghj 7) 3 w x 4 d x 2 h x yz 24 dhwyz 8) 7 pqr x 4 abc x 2 h 56 abchpqr

0 7 S e p t e m b e r 2 0 2 1 Questions – reverse multiplication 1) 7 ab x 10 c ___ = 70 abc 2) 3 f x ___ 4 g x 5 h = 60 fgh d = 3 abcd 3) 3 abc x ___ 4 = 20 g 4) 5 g x ___ p x 4 = 20 mnp 5) 5 mn x ___ 6) 5 f x 4 h ___ x 2 g = 40 fgh 7) 3 w x ___ 4 x 2 v x yz = 24 vwyz 8) 4 bc x 10 e ___ x 2 ad = 80 abcde Page 4

0 7 Dividing S e p t e m b e r 2 0 2 1 Algebraic Terms Simplify: 8 a ÷ 4 = 2 a 10 ab ÷ 2 a = 20 pq pq = 5 b 20

Powers Rules axa= a 2 axaxaxa= a 4 But, what is a 2 x a 4? 6 It’s (a x a) x (a x a x a) = a What did you do with the powers? You added them! Rule 1: When you multiply powers of the same letter or number you add the indices…

0 7 S e p t e m b e r 2 0 2 1 Indices Questions a 3 x a 6 x a 2 = c 3 x c 5 x c = 2 y 2 x 4 y 5 = a 11 c 9 8 y 7 3 m 3 x 4 m 5 = 12 m 8

Harder Indices Questions Q 1. 2 a 3 b 6 x a 6 b 2 = 2 a 9 b 8 Q 2. 3 c 5 d 4 x 5 c 2 d 4 = 15 c 7 d 8 Q 3. 2 ab 4 x 4 a 2 b 3 8 a 3 b 7 Q 4. = 3 mnp 3 x 4 mn 2 p 5 = 12 m 2 n 3 p 8

Powers axaxa= a 5 a 3 But, what is a 5 a 3? It’s (a x a x a) (a x a) = a 2 What did you do with the powers? You subtracted them! Rule 2: When you divide powers of the same letter or number you subtract the indices…

Indices Questions a 6 a 2 = a 4 c 3 c 5 c-2 3 y 2 x 4 y 5 2 y 3 = 6 y 4

Harder Indices Questions Q 1. 4 a 6 x 8 a 2 = 2 a 9 16 a-1 Q 2. 30 y 2 x 4 y 5 = 6 x y 4 20 y 3

0 7 S e p t e m b e r 2 0 2 1 Powers a x a =a 3 What do you think is… (a 3)2 = a 3 x a 3 =a 6 what did you do with the powers here? multiplied them! Rule 3: When you raise a power by another power (separated by brackets) you multiply the indices…

Indices Questions a 14 Q 1. (a 2)4 x (a 3)2 = Q 2. Q 3. 4(a 2)3 = 4 a 6 (4 a 2)3 = 64 a 6 (5 ab 3)2 = 25 a 2 b 6 Q 4.

Have you really understood indices? ? We’ll see… Simplify this…