1. Multiplication in Algebra Involving Indices

2. 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

3. 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

4. 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

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

6. 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

7. 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

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

9. 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

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

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

12. 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

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

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