1. Powers and indices: Fractional Indices
Silent
Teacher
Intelligent Practice
Narration
Your Turn = =
𝑥 1 𝑦 =
Example

2. Worked Example
Your Turn = =
= 4 2 16

3.
− 1 3
− 4 3
9 1 3
9 1 4
9 1 2
9 3 4
Evaluate
4 1 2
2 1 2
1 1 2
8 1 2
8 1 3
8 2 3
8 4 3

4.
− 1 3
− 4 3
9 1 3
9 1 4
9 1 2
9 3 4
Evaluate 3
3 9
4 1 2
2 1 2
1 1 2
8 1 2
8 1 3
8 2 3
8 4 3
±10 30 ±2
± 200 9
± 3
±20
900 ±3 ±2
±3 3 81
± 2
3 40 ± =± = ±1
2 3
± 2 3 =±
± 8
3 2
± 2 9 2 =± 4
16 81 ± 16
± 2 5
16 81

5. Evaluate
64 𝑥
64 𝑥
64 𝑥
64 (𝑥 2 ) 1 6
64 (𝑥 ) 6
64 (𝑥 ) −6
64 (𝑥 4 ) 1 12
( 64 𝑥 4 ) 1 12
(64𝑥 4 𝑦 3 ) 1 12
64(𝑥 𝑦 )
64 𝑥
64𝑥 1 3
64 𝑥 1 3
64 𝑥 − 1 3
64𝑥 − 1 3
64𝑥 − 1 2
64 𝑥 − 1 2
64 𝑥 1 2
64 𝑥
64 𝑥

6. Evaluate
64 𝑥
64 𝑥
64 𝑥
64 (𝑥 2 ) 1 6
64 (𝑥 ) 6
64 (𝑥 ) −6
64 (𝑥 4 ) 1 12
( 64 𝑥 4 ) 1 12
(64𝑥 4 𝑦 3 ) 1 12
64(𝑥 𝑦 )
64 𝑥
64𝑥 1 3
64 𝑥 1 3
64 𝑥 − 1 3
64𝑥 − 1 3
64𝑥 − 1 2
64 𝑥 − 1 2
64 𝑥 1 2
64 𝑥
64 𝑥 4𝑥
±8 6 𝑥
4 3 𝑥
±4 6 𝑥
64 3 𝑥
±2 𝑥
64 3 𝑥
±2 3 𝑥
1 4 3 𝑥
2 𝑥 2
± 1 8 𝑥
2 𝑥 2
± 1 𝑥
64 3 𝑥
±64 𝑥
2 3 𝑥
± 𝑥 3 𝑜𝑟± 𝑥 3
2 3 𝑥 4 𝑦
±8 𝑥 3 𝑜𝑟±8 𝑥 3
64 3 𝑥 4 𝑦