Question

Вычислить: (8^(2/3)+(1/9)^(-3/2)+√(125^(2/3)))^(1/2)

Answer 1

$(8^{frac{2}{3}}+(frac{1}{9})^{-frac{3}{2}}+sqrt{125^{frac{2}{3}}})^{frac{1}{2}}=sqrt{(8^{frac{1}{3}})^2+9^{frac{3}{2}}+(125^{frac{2}{3}})^{frac{1}{2}}}=\\sqrt{(sqrt[3]{8})^2+(9^{frac{1}{2}})^3+125^{frac{1}{3}}}=sqrt{2^2+(sqrt{9})^3+sqrt[3]{125}}=sqrt{4+3^3+5}=\\sqrt{9+27}=sqrt{36}=6$