Powers and indices: Fractional Indices Silent Teacher Intelligent Practice Narration Your Turn 4 1 2 = 8 2 3 = 𝑥 1 𝑦 = Example

Worked Example Your Turn 64 3 2 64 2 3 = 64 1 3 2 = 3 64 2 = 4 2 16

27 1 3 27000 1 3 27 2 3 27000 2 3 27 4 3 27 40 3 8 27 1 3 8 27 − 1 3 8 27 4 3 27 8 − 4 3 9 1 3 16 1 4 9 1 4 9 1 2 9 3 4 1 9 3 4 16 9 1 4 16 9 1 4 16 9 1 4 0.16 1 2 Evaluate 100 1 2 200 1 2 400 1 2 4 1 2 2 1 2 1 1 2 8 1 2 8 1 3 8 2 3 8 4 3

27 1 3 27000 1 3 27 2 3 27000 2 3 27 4 3 27 40 3 8 27 1 3 8 27 − 1 3 8 27 4 3 27 8 − 4 3 9 1 3 16 1 4 9 1 4 9 1 2 9 3 4 1 9 3 4 16 9 1 4 16 9 1 4 16 9 1 4 0.16 1 2 Evaluate 3 3 9 100 1 2 200 1 2 400 1 2 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 3 3 =± 3 9 =12157665459056928801 ±1 2 3 ± 2 3 =± 3 3 ± 8 3 2 ± 2 9 2 =± 16 3 3 4 16 81 ± 16 3 16 ± 2 5 16 81

Evaluate 64 𝑥 1 3 1 2 64 𝑥 1 2 1 3 64 𝑥 3 1 6 64 (𝑥 2 ) 1 6 64 (𝑥 1 3 ) 6 64 (𝑥 1 3 ) −6 64 (𝑥 4 ) 1 12 ( 64 𝑥 4 ) 1 12 (64𝑥 4 𝑦 3 ) 1 12 64(𝑥 4 11 𝑦 6 22 ) 11 12 64 𝑥 3 1 3 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 1 2 3 64 𝑥 3 1 2

Evaluate 64 𝑥 1 3 1 2 64 𝑥 1 2 1 3 64 𝑥 3 1 6 64 (𝑥 2 ) 1 6 64 (𝑥 1 3 ) 6 64 (𝑥 1 3 ) −6 64 (𝑥 4 ) 1 12 ( 64 𝑥 4 ) 1 12 (64𝑥 4 𝑦 3 ) 1 12 64(𝑥 4 11 𝑦 6 22 ) 11 12 64 𝑥 3 1 3 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 1 2 3 64 𝑥 3 1 2 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 ± 64 3 𝑥 3 𝑜𝑟± 64 3 𝑥 3 2 3 𝑥 4 𝑦 ±8 𝑥 3 𝑜𝑟±8 𝑥 3 64 3 𝑥 4 𝑦