Question

comparati a si b , unde a = ( 4 la puterea 10 - 4 la puterea 9 ) x ( 4 la puterea 9 - 4 la puterea 8 ) x .... x ( 4 la puterea 2 - 4 la puterea 1 ) si b = 3 x 2 la puterea 90 x 81 la puterea 2

Answer 1

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

b = 3 * 2^90 * 81^2 = 3 * 2^90 * (3^4)^2 = 3 * 2^90 * 3^8 = 2^90 * 3^9

Se observa ca a = b