This document provides examples and rules for performing operations with indices and fractional indices. It explains that multiplying terms keeps the base and adds the indices, dividing terms keeps the base and subtracts the indices. Negative indices result in the reciprocal of the base to the power of the absolute value of the index. Fractional indices mean the root is on the bottom and the top number is the power. It also gives examples like square root problems can be written as indices of one-half and provides practice problems for the reader to try.

1. Block 1
Indices Summary

2. Indices
Another word for powers
Multiplying
am
X an
Dividing
am
÷ an
= a= am+nm+n
= a= am – nm – n

3. y2
X y8
= y10
44
X 47
= 411
2b9
X 5b3
= 10b12
t7
÷ t3
= t4
18m6
3m2
= 6m4

4. Another Rule
(ya
)b
(g3
)2
Please Note not the same as g3
X g2
= yab
= g6
= g5

5. Negative Indices
a0
= 1
a-m
= 1
am
so 12m-3 = 12 X 1
m3
= 12
m3
1
-a 2
= 1

6. Fractional Indices
• The root still on the bottom
• Top number is the power.
= (e
√a )f
f
/e
16
= (2
√16)
= 4
= 64
33
//22
33
33
a

7. Two to Remember

8. Save Brain Energy
Switch to
half power
√x
= x½
root of the
problem

9. x-2
I’m Not
Sure This
is Right?
Negative
Thinking
= 1
x2
I’m
Positive

10. You Try
1. 16 2. 1000
3. 32 4. 49
5. 64 6. 81
33
//22
33
//22
22
//33
22
//33
44
//55
¾
= 64 = 100
= 16 = 343
= 16 = 27