Question

Calculati:   (3³²:3²+2²x2²⁵-2003°):(27¹⁰+8⁹-324:18²)

Answer 1

(3³²:3²+2²x2²⁵-2003°):(27¹⁰+8⁹-324:18²)=(3³²⁻²+2²⁺²⁵-1):(3³°+2²⁷-1)=(3³°+2²⁷-1):(3³°+2²⁷-1)=1
27¹°=(3³)¹°=3³°
8⁹=(2³)⁹=2²⁷
18²=324
324:324=1

Answer 2

      
$\frac{ 3^{32}: 3^{2}+ 2^{2}*2^{25}- 2003^{0}}{ 27^{10}+ 8^{9}-324: 18^{2}}= \\ \\ =\frac{ 3^{32-2}+ 2^{2+25}- 2003^{0}}{ ( 3^{3} )^{10}+ ( 2^{3} )^{9}-18^{2}: 18^{2}}= \\ \\ =\frac{ 3^{32-2}+ 2^{2+25}- 2003^{0}}{ 3^{3*10}+ 2^{3*9}-18^{2-2}}= \\ \\=\frac{ 3^{30}+ 2^{27}- 2003^{0}}{3^{30}+ 2^{27} -18^{0}}=\\ \\ =\frac{ 3^{30}+ 2^{27}- 1}{3^{30}+ 2^{27} -1}=1$