1. Methods In Algebra
Like terms can be added or subtracted, unlike
terms cannot.

2. Index Laws
a m  a n  a mn

3. Index Laws
a m  a n  a mn
a m  a n  a mn

4. Index Laws
a m  a n  a mn
a m  a n  a mn
a 
m n
 a mn

5. Index Laws
a m  a n  a mn
a m  a n  a mn
a 
m n
 a mn
a0  1

6. Index Meaning
 : top of the fraction

7. Index Meaning
 : top of the fraction
 : bottom of the fraction

8. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power

9. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power
root

10. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power
 b xa
root
OR
  x
b
a

11. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power
 b xa
root
OR
  x
b
e.g. (i ) x 3 
a

12. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power
 b xa
root
OR
  x
b
e.g. (i ) x
3
1
 3
x
a

13. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power
 b xa
root
OR
  x
b
e.g. (i ) x
3
1
 3
x
a
(ii ) a 5b 7 

14. Index Meaning
 : top of the fraction
 : bottom of the fraction
x
a
b
power
 b xa
root
OR
  x
b
e.g. (i ) x
3
1
 3
x
a
(ii ) a 5b 7
a5
 7
b

15. 3
(iii ) x  4 a 9b  2 
4

16. 3
(iii ) x  4 a 9b  2
4
3a 9
 4 2
4x b

17. 3
(iii ) x  4 a 9b  2
4
1
4
(iv) x 
3a 9
 4 2
4x b

18. 3
(iii ) x  4 a 9b  2
4
1
4
(iv) x 
4
x
3a 9
 4 2
4x b

19. 3
(iii ) x  4 a 9b  2
4
1
4
(iv) x 
2
3
(v ) y 
4
x
3a 9
 4 2
4x b

20. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
y2
(iv) x 
(v ) y 
3a 9
 4 2
4x b

21. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
y2
(iv) x 
(v ) y 
3
2
(vi ) x 
3a 9
 4 2
4x b

22. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
y2
(iv) x 
(v ) y 
3
2
(vi ) x 
x3
3a 9
 4 2
4x b

23. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
3a 9
 4 2
4x b
y2
(iv) x 
(v ) y 
3
2
(vi ) x 
x3
 x2 x

24. 3
(iii ) x  4 a 9b  2
4
1
4
(iv) x 
2
3
(v ) y 
3
2
(vi ) x 
4
3
3a 9
 4 2
4x b
x
x2
x3
 x2 x
x x

25. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
3a 9
 4 2
4x b
y2
(iv) x 
(v ) y 
3
2
(vi ) x 
x
3
 x2 x
x x
see
OR
3
2
x 

26. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
3a 9
 4 2
4x b
y2
(iv) x 
(v ) y 
3
2
(vi ) x 
x
3
 x2 x
x x
see
OR
3
2
x 
1
1
2
x
think

27. 3
(iii ) x  4 a 9b  2
4
1
4
4
x
2
3
3
3a 9
 4 2
4x b
y2
(iv) x 
(v ) y 
3
2
(vi ) x 
x
3
see
3
2
x 
OR
1
1
2
x
x x
 x2 x
x x
think
1
x
and
x
1
2

28. (vii ) m
27
4


29. (vii ) m
27
4
64
3
 m m

30. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2

31. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
2

32. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
2 n6

33. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
p 500
2 n6

34. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
p 500
2 n 6 28 q

35. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
p 500 c 6 c
2 n 6 28 q

36. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
p 500 c 6 c r 69
2 n 6 28 q

37. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
 2
(ix)  
 3
2

p 500 c 6 c r 69
2 n 6 28 q

38. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
 2
(ix)  
 3
2
 3
  
 2
2
p 500 c 6 c r 69
2 n 6 28 q

39. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
 2
(ix)  
 3
2
 3
  
 2
9

4
2
p 500 c 6 c r 69
2 n 6 28 q

40. (vii ) m
27
4
64
3
 m m
1
7
1 6 500  28 6 69
(viii ) n p q c r 
2
 2
(ix)  
 3
2
 3
  
 2
9

4
p 500 c 6 c r 69
2 n 6 28 q
2
Exercise 1A; 1c, 2d, 3b, 4d, 5b, 6ad, 7bc, 8a, 9b, 10d, 11cf,
12ac, 13bd, 15, 17, 18*
Exercise 6A; 1adgi, 2behj, 3ace, 4ace, 5bdfh, 6ace, 7adgj,
8behj, 9bd