Question

Compute 

(i) 102⁴ 

(ii) 99⁴ 

(iii) 9⁷

Answer 1

(i) 102⁴ = (100 + 2)⁴ = (10 + 2)⁴

= 1(10⁸) + 4(10⁶)(2) + 6(10⁴)(4) + 4(10²)(8) + 16 

= 100000000 + 8000000 + 240000 + 3200 + 16 

= 108243216

(ii) 99⁴ = (100 – 1)⁴ = (10² – 1)⁴

= 1(10⁸) + 4(10⁶)(-1) + 6 (10⁴)(1) + 4(10⁴)(-1) + (-1)⁴ 

= 100000000 – 4000000 + 60000 – 400 + 1 

= 100060001 – 4000400 = 96059601

(iii) 9⁷ = (10 – 1)⁷

= 1(10000000) + 7(1000000)(-1) + 21(100000)(1) + 35(10000)(-1) + 35(1000)(1) + 21(100)(-1) + 7(10) (1) + 1(-1) 

= 10000000 – 7000000 + 2100000 – 350000 + 35000 – 2100 + 70 – 1 

= 12135070 – 7352101 = 4782969