This is a quick tutorial for students seeking to use the first, second and third index law at a more intermediate level.

2. x 3 × x 4 which is the same as x 3. x 4
Use the 1st Index law: a × a = a
m n m+n
In this example: a = 1 and 1; m = 3 and n = 4
So now you just substitute the values into the formula.
=x 3+4
Answer = x 7

3. 3
x
which is the same as x3 ÷ x1 (or just x− Remember x1 = x)
x
am m− n
Use the 2nd Index law: n = a
a
In this example: a = 1 and 1 (These are the numbers in front of the pronumerals (the letters); m = 3 and n = 1
So now you just substitute the values into the formula.
= x3−1
Answer = x 2

4. 59 x 53 = 512 = 59
53 53
76 x 77 = 713 = 79
74 74

5. a6 x a4 = a10
b5 x b7 = b12
c5 x c3 = c8 = c4
c4 c4
a5 x a3 = a8 = a-2
a4 x a6 a10

6. How could you get an answer of 30?
35 ÷ 35 = 35-5 = 30
30 = 1 General Rule
a0 = 1

7. a 3b 4
3 3
=b
ab
But how?
am
Appply the index rule: n = a m−n
a
= a 3−3 × b 4−3
= a 0 × b1
= 1× b
or just b
Answer = b

8. 2a3 x 3a4 = 2 x 3 x a3 x a4 = 6a7
8a6 ÷ 4a4 = (8 ÷ 4) x (a6 ÷ a4) = 2a2
28a 62
4a 4

9. 4x 3
which is the same as 4x 3 ÷ 3x
3x
am
Use the 2nd Index law: n = a m−n
a
In this example: a = 4 and 3; m = 3 and n = 1
So now you just substitute the values into the formula.
4x 3−1
=
3
4x 2
Answer =
3

10. This can be for the next tutorial.
Something to look forward to.