Вычислить: 1) 2^-2*64^1/3-64^1/3:2^-4 2) 8^1/4:2^-4+3^-3*81^1/4 3) √4+2*√2-∛4-2*√2 4) √15+√46*√17-√46

Вычислим значения выражений:

1) 2^ (-2) * 64^ (1/3) - 64^ (1/3) : 2^ (-4) = 64^ (1/3) * (2^ (-2) - 1/2^ (-4)) = (4^3) ^ (1/3) * (1/2^2 - 1/2^4) = 4^ (3 * 1/3) * (1/4 - 1/16) = 4 * (4 - 1) / 16 = 4 * 3/16 = 3/4;

2) 8^ (1/4) : 2^ (-4) + 3^ (-3) * 81^ (1/4) = 2^ (3/4) / 2^ (-4) + 3^ (-3) * 3^ (4/4) = 2^3/2^4 * 2^4 + 3^ (-3) * 3 = 2^3 + 3^ (-3 + 1) = 8 + 1/9 = 8 1/9;

3) √4 + 2 * √2 - ∛4 - 2 * √2 = √4 - ∛4 = 2 - 2^ (2/3);

4) √15 + √46 * √17 - √46 = √15 + √46 * (√17 - 1).