Multiplication in Algebra Involving Indices

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

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

Questions – reverse multiplication Tuesday, 01 January 2019 Questions – reverse multiplication 1) 7ab x ___ = 70abc 2) 3f x ___ x 5h = 60fgh 3) 3abc x ___ = 3abcd 4) 5g x ___ = 20g 5) 5mn x ___ x 4 = 20mnp 6) 5f x ___ x 2g = 40fgh 7) 3w x ___ x 2v x yz = 24vwyz 8) 4bc x ___ x 2ad = 80abcde 10c 4g d 4 p 4h 4 10e

Dividing Algebraic Terms Tuesday, 01 January 2019 Dividing Algebraic Terms Simplify: 8a ÷ 4 = 10ab ÷ 2a = 20pq pq = 2a 5b 20

Powers Rules a2 a4 a6 a x a = Rule 1: a x a x a x a = But, what is a2 x a4? It’s (a x a) x (a x a x a x a) = What did you do with the powers? You added them! a2 Rule 1: When you multiply powers of the same letter or number you add the indices… a4 a6

Indices Questions a11 c9 8y7 12m8 a3 x a6 x a2 = c3 x c5 x c = Tuesday, 01 January 2019 Indices Questions a3 x a6 x a2 = c3 x c5 x c = 2y2 x 4y5 = 3m3 x 4m5 = a11 c9 8y7 12m8

Harder Indices Questions 2a3b6 x a6b2 = 3c5d4 x 5c2d4 = 2ab4 x 4a2b3 = 3mnp3 x 4mn2p5 = Q1. 2a9b8 15c7d8 Q2. Q3. 8a3b7 12m2n3p8 Q4.

Powers a5 a3 a2 a x a x a x a x a = a x a x a = Rule 2: But, what is a5 a3? It’s (a x a x a x a x a) (a x a x a) = What did you do with the powers? You subtracted them! a5 Rule 2: When you divide powers of the same letter or number you subtract the indices… a3 a2

Indices Questions a6  a2 = c3  c5 = 3y2 x 4y5 2y3 a4 c-2 6y4

Harder Indices Questions 4a6 x 8a2 = 2a9 30y2 x 4y5 = 6 x y4 16a-1 Q2. 20y3

Powers a3 a6 a x a x a = What do you think is… (a3)2 Rule 3: Tuesday, 01 January 2019 Powers a x a x a = What do you think is… (a3)2 = a3 x a3 = a3 Rule 3: When you raise a power by another power (separated by brackets) you multiply the indices… what did you do with the powers here? multiplied them! a6

Indices Questions a14 Q1. 4a6 Q2. Q3. 64a6 Q4. 25a2b6 (a2)4 x (a3)2 =

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