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Question

Compute these powers:

(a) 305

(b) 404

(c) 703

(d) 2003

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Solution

(a) (30)5 = 30 × 30 × 30 × 30 × 30

= (3 × 10) × (3 × 10) × (3 × 10) × (3 × 10) × (3 × 10)

= (3 × 3 × 3 × 3 × 3) × (10 × 10 × 10 × 10 × 10)

= 35× 105

= 243 × 100000

= 24300000

(b) (40)4 = 40 × 40 × 40 × 40

= (4 × 10) × (4 × 10) × (4 × 10) × (4 × 10)

= (4 × 4 × 4 × 4) × (10 × 10 × 10 × 10)

= 44× 104

= 256 × 10000

= 2560000

(c) (70)3 = 70 × 70 × 70

= (7 × 10) × (7 × 10) × (7 × 10)

= (7 × 7 × 7) × (10 × 10 × 10)

= 73× 103

= 343 × 1000

= 343000

(d) (200)3 = 200 × 200 × 200

= (2 × 100) × (2 × 100) × (2 × 100)

= (2 × 2 × 2) × (100 × 100 × 100)

= (2 × 2 × 2) × (10 × 10 × 10 × 10 × 10 × 10)

= 23× 106

= 8 × 1000000

= 8000000


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