Question

Comparati numerele:a=[(2^8)^3:(2^6+2^6):8-8^6:4^5:16]:2^12+2 si b=3^46:[9^22+3^20•27^8+9^30:81^4]-2^23:(2^22+2^22)

Answer 1

a=[(2^8)^3:(2^6+2^6):8-8^6:4^5:16]:2^12+2 si
b=3^46:[9^22+3^20•27^8+9^30:81^4]-2^23:(2^22+2^22)

a
=(2^24:2^7:2^3-2^18:2^10:2^4):2^12+2
=[2^(24-7-3)-2^(18-10-4)]:2^12+2
=(2^14-2^4):2^12+2
=2^4(2^10-1):2^12+2
=(2^10-1):2^8+2
=2^(10-8)-2^(0-8)+2
=2^2-1/2^8+2
=4+2-1/256
=6-1/256
=6-0.003906
=5.996094

b
=3^46:(3^44+3^20 x 3^24+3^60:3^16)-2^23:(2^22 x 2^22)
=3^46:[3^44+3^(20+24)+3^(60-16)]-2^23:2^22(1+1)
=3^46:(3^44+3^44+3^44)-2^23:(2^22 x 2)
=3^46:[3^44(1+1+1)]-2^23:2^(22+1)
=3^46:(3^44 x 3)-2^23:2^23
=3^46:3^(44+1)-2^(23-23)
=3^46:3^45-2^0
=3^(46-45)-1
=3^1-1
=3-1
=2

a>b
5.996094>2