Question

Fie numerele a =(1+2+3+....+999) x2:10 la puterea a 2 și b= (2 la puterea a 17 x 5 la puterea a 17)puterea 11 :100 la puterea 93 :10.
Calculați valoarea lui c=2x(a+b)-1000.

Answer 1

a = ( 1 + 2 + 3 + .... + 999 ) x 2 : 10²

a = [ 999 x ( 1 + 999 ) : 2] x 2 : 100

a = ( 999 x 1 000 : 2 ) x 2 : 100

a = 9 990

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b = ( 2¹⁷ x 5¹⁷ )¹¹  : 100⁹³ : 100

b = ( 2 x 5 ) ¹⁷ ˣ ¹¹ : ( 10² )⁹³ : 10

b = 10 ¹⁸⁷ : 10¹⁸⁶ : 10

b = 10 ⁽ ¹⁸⁷ ⁻ ¹⁸⁶ ⁻ ¹ ⁾

b = 10⁰

b = 1

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c = 2 × ( a + b ) - 100

c = 2 × ( 9 990 + 1 ) - 100

c = 2 × 9 991 - 100

c = 19 982 - 100

c = 19 882

Answer 2

a = (1 + 2 + 3 + ...+ 999) × 2 : 10^2

a = 999 × (999 + 1) : 2 × 2 : 100

a = 999 × 1000 : 100

a = 999 × 10

a = 9 990
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b = (2^17 × 5^17)^11 : 100^93 : 10

b = [(2 × 5)^17]^11 : (10^2)^93 : 10

b = 10^187 : 10^186 : 10

b = 10^(187 - 186 - 1)

b = 10^0

b = 1
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c = 2 × (a +b) - 1000

c = 2 × ( 9 990 + 1) - 1000

c = 2 × 9 991 - 1000

c = 19 982 - 1000

c = 18 982
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