Algebraic Operations

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Algebraic Operations
S5 Int2
Adding / Sub Indices
Negative Indices
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Fraction Indices
Harder Indices
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Starter Questions
S5 Int2
1. Simplify the following fractions
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Algebraic Operations
S5 Int2
Learning Intention
Success Criteria

1. To explain how to multiply and divide indices by
   adding / subtracting powers.

1. Understand basic rules for indices.

2. Simplify indices.
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4
Indices
S5 Int2
an is a short hand way of writing a x a x a .
(n factors) a is called the base number and n
is called the index number
Calculate 23 x 22
x 2 x 2
2 x 2 x 2
32
Calculate 25
32
Can you spot the connection !
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Indices
S5 Int2
Calculate 43 42
4 x 4 x 4
4
4 x 4
Calculate 41
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Can you spot the connection !
am x an a(m n) simply add powers
am an a(m - n) simply subtract powers
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What Goes In The Box ?
S5 Int2
b3 x b5
f4 x g5
b8
y9 y5
a3 x a0
y4
Exercise 11 Page 209
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Starter Questions
S5 Int2
1. Simplify the following fractions
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Algebraic Operations
S5 Int2
Learning Intention
Success Criteria

1. To explain how to hand fractional indices of
   powers.

1. Understand basic rules for fractional indices.

2. Simplify fractional indices.
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9
Fractions as Indices
S5 Int2
More Rules
By the division rule
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Fractions as Indices
S5 Int2
More Rules
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Fractions as Indices
S5 Int2
More Rules
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Fractions as Indices
S5 Int2
Exercise 12 Page 210
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Starter Questions
S5 Int2
1. Rationalise the denominator
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Algebraic Operations
S5 Int2
Learning Intention
Success Criteria

1. To explain how to hand fractional indices of
   powers.

1. Understand basic rules for fractional indices.

2. Simplify fractional indices.
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15
Fractions as Indices
S5 Int2
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Fractions as Indices
S5 Int2
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Fractions as Indices
S5 Int2
In general we have
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Fractions as Indices
S5 Int2
Examples Simplify the following
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Fractions as Indices
S5 Int2
Exercise 13 Page 211
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Starter Questions
S5 Int2
1. Rationalise the denominator
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Algebraic Operations
S5 Int2
Learning Intention
Success Criteria

1. To show how to simplify harder fractional indices.

1. Simplify harder fractional indices.

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22
Fractions as Indices
S5 Int2
Final Rule
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Fractions as Indices
S5 Int2
Examples
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Fractions as Indices
S5 Int2
Examples
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Fractions as Indices
S5 Int2
Example Change to index form
Example Change to surd form
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Fractions as Indices
S5 Int2
Exercise 213 Page 213