1. ©2009 – Not to be sold/Free to use
Stage 5
Year 9
Rational
Numbers
Fractional
Indices
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©2009 – Not to be sold/Free to use

2. Rule: a = n√a 9½ = 2√9 = √9 = 3 Fractional Index 1 n 2
MathScape Yr Exercise 8.10 Q.1, 2 2

3. Rule: a = n√a 8 = 3√9 = 3 Fractional Index 1 n 1 3 3
8 =
3√9 = 3
MathScape Yr Exercise 8.10 Q.1, 2 3 3

4. Rule: a = n√a 16 = 4√16 = 2 Fractional Index 1 n 1 4 4
16 =
4√16 = 2
MathScape Yr Exercise 8.10 Q.1, 2 4 4

5. Evaluating Numbers in Index Notation
Exercises
a) 3 = 3
b) 4 = 4
c) 7 = 7
d) 5 = 5
e) 3 = 3
f) 8 = 8 1 2 4 3
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6. Rule: a = n√a 9 = (√9)3 = 33 = 27 Fractional Index m n 3 2 6
9 =
(√9)3 =
33 = 27
MathScape Yr Exercise 8.10 Q.1, 2 6 6

7. Rule: a = n√a 8 = (3√8)2 = 22 = 4 Fractional Index m n 2 3 7
8 =
(3√8)2 =
22 = 4
MathScape Yr Exercise 8.10 Q.1, 2 7 7

8. Evaluating Numbers in Index Notation
Exercises
a) 5 = 5
b) 6 = 6
c) 2 = 2
d) 3 = 3
e) 7 = 7
f) 9 = 9 2 3 4 5 7 2 5 3 3 3 4 7
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9. Rule: a = n√a 4 = (√4)-3 = 2-3 = 8-1 1 8 Fractional Index -m n -3 2
4 =
(√4)-3 =
2-3 =
8-1
MathScape Yr Exercise 8.10 Q.1, 2 1 8 9

10. Rule: a = n√a 27 = (3√27)-2 = 3-2 = 9-1 1 9 Fractional Index -m n -2 3
27 = -2 3
(3√27)-2 =
3-2 =
9-1
MathScape Yr Exercise 8.10 Q.1, 2 1 9 10

11. Evaluating Numbers in Index Notation
Exercises 1 1 -3 2 1
a) 16 = = = 3 3 2 16 4 64 1 -4 3 1 1
b) 8 = = = 4 3 27 4 3 81
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