Question

Calculati: a) (2 la puterea 11 - 2 la puterea 10) : la 2 la puterea 10
b) 4 la puterea 47+2 la puterea 93+16 la puterea 23-7*(2 la puterea 4) la puterea 23
c) 3 la puterea 2010-3 la puterea 2009-3 la puterea 2008-5*9 la puterea 1004
d) 3 la puterea 6-2*3 la puterea 5-2*3 la puterea 4-2*3 la puterea 3-2*3 la puterea 2-2*3-1

Answer 1

a) 2^11 : 2^10 - 2^10 : 2^10 = 2 - 1=1
b) 4^47 + 2^93 + 16^23 -7×(2^4)^23 = (2²)^47 + 2^93 + (2^4)^23 - 7×2^92 =
= 2^94 + 2^93 + 2^92 - 7×2^92 = 2^93(2 + 1) - 6 × 2^92 = 3×2^93 - 6×2^92 =
= 3×2^92(2 - 3) = - 3×2^92
c) 3^2010 - 3^2009 - 3^2008 - 5×9^1004 =
= 3^2008(3² - 3 -1) - 5×(3²)^1004 = 5×3^2008 - 5×3^2008 = 0
d) 3^6 - 2×3^5 - 2×3^4 - 2×3³ - 2×3² - 2×3 - 1 =
= 3^5 ( 3 - 2) - 2×3³ (3 + 1) - 2×3(3+ 1) - 1=
= 3^3 - 2³×3³ - 2³×3 - 1= 3³(1 - 2³) - 2³×3 - 1= -7×3³ - 8×3 - 1= - 7×27 - 24 - 1 = - 189 - 25 = -214