Question

Comparati numerele a si b, unde a=3*2 la puterea 90*81 la puterea 2 si b=(4 la puterea 10-4 la puterea 9)*(4 la puterea 9-4 la puterea 8)*(4 la puterea 8- 4 la puterea 7)*...*(4 la puterea 2-4 la puterea 1)

Answer 1

a=3*2^90*81^2 =3*2^90*3^8 =2^90*3^9

b=(4^10-4^9)*(4 ^9-4^8)*(4^8- 4^7)*...*(4^2-4^1) =
=4^9*(4^1-4^0)*4^8*(4 ^1-4^0)*4^7*(4^1- 4^0)*...*4^1*(4^1-4^0) =
=4^9*(4-1)*4^8*(4-1)*4^7*(4-1)*...*4^1*(4-1) =
=4^9*3*4^8*3*4^7*3*...*4^1*3) =
=3^9 *4^(1+2+3+...+9)=
=3^9 *4^(9*10/2)=
=3^9 *4^45=
=3^9 *2^90

rezulta a=b =2^90 *3^9