Odpowiedź:
1.3.
e) √75 : 3^(1 1/3) * 3^(5/6) = √75 : 3^(4/3) * 3^(5/6) = √75 * 3^(5/6) / 3^(4/3) = √75 * 3^(5/6) / 3^(3/6) = √75 : [3^(5/6 * 3^(3/6)] = √75 : 3^(1/2) = √75 / √3 = 5√3 / √3 = 5
f) [18^(-2/3)*∛4 : 27^(-1/6)](-1,2) = [(3^2*2)^(-2/3) * (2^2)^1/3 : (3^3)^(-1/6)]^(-6/5) = [3^(-4/3) * 2^(-2/3) * 2^2/3 : 3^(-1/2)]^(-6/5) =
= [3^(-4/3+1/2)]^(-6/5) = [3^(-8/6+3/6)]^(-6/5) = [3^(-5/6)]^(-6/5) = 3^1 = 3
Szczegółowe wyjaśnienie:
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Odpowiedź:
1.3.
e) √75 : 3^(1 1/3) * 3^(5/6) = √75 : 3^(4/3) * 3^(5/6) = √75 * 3^(5/6) / 3^(4/3) = √75 * 3^(5/6) / 3^(3/6) = √75 : [3^(5/6 * 3^(3/6)] = √75 : 3^(1/2) = √75 / √3 = 5√3 / √3 = 5
f) [18^(-2/3)*∛4 : 27^(-1/6)](-1,2) = [(3^2*2)^(-2/3) * (2^2)^1/3 : (3^3)^(-1/6)]^(-6/5) = [3^(-4/3) * 2^(-2/3) * 2^2/3 : 3^(-1/2)]^(-6/5) =
= [3^(-4/3+1/2)]^(-6/5) = [3^(-8/6+3/6)]^(-6/5) = [3^(-5/6)]^(-6/5) = 3^1 = 3
Szczegółowe wyjaśnienie: