Question

12 repede va rog frumos​

Answer 1

a) (2x)×(2x)²×(2x)³×...×(2x)¹⁰⁰⁰

= (2x)^(1+2+3+...+1000)

= (2x)^(1000×1001/2)

= (2x)^(1001000/2)

= 2x⁵⁰⁰⁵⁰⁰

b) (-4x)×(-4x)³×(-4x)⁵×...×(-4x)¹⁰⁰¹

= (-4x)^(1+3+5+...1001)

1+3+5+...1001 = (1+2+3+4+...1001) - (2+4+6+...+1000)

= 1001×1002/2 - 2(1+2+3+...+500)

= 1003002/2 - 2(500×501/2)

= 501501 - 500×501 = 501501 - 250500

= 251001

= (-4x)²⁵¹⁰⁰¹

c) (-3a)²×(-3a)⁴×(-3a)⁶×...×(-3a)¹⁰⁰⁰

= (-3a)^(2+4+6+...+1000)

2+4+6+...+1000 = 2(1+2+3+...+500) = 2(500×501)/2 = 500×501 = 250500

= (-3a)²⁵⁰⁵⁰⁰