Tính:

    a). \[\sqrt[3]{{27}} - \sqrt[3]{{ - 8}} - \sqrt[3]{{125}};\]                                                b). \[\frac{{\sqrt[3]{{135}}}}{{\sqrt[3]{5}}} - \sqrt[3]{{54}}.\sqrt[3]{4}.\]

a) Ta có \(\sqrt[3]{{{x^3} + 1 + 3x\left( {x + 1} \right)}} = \sqrt[3]{{{{(x + 1)}^3}}} = x + 1\).    

b) \(\frac{{x + 1}}{{\sqrt[3]{{{x^2}}} - \sqrt[3]{x} + 1}} = \frac{{\left( {\sqrt[3]{x} + 1} \right)\left( {\sqrt[3]{{{x^2}}} - \sqrt[3]{x} + 1} \right)}}{{\sqrt[3]{{{x^2}}} - \sqrt[3]{x} + 1}} = \sqrt[3]{x} + 1\).

Ta có: \[\sqrt[3]{{512}} = \sqrt[3]{{{8^3}}} = 8.\]

\[\sqrt[3]{{ - 729}} = \sqrt[3]{{ - {9^3}}} =  - 9.\]

\[\sqrt[3]{{0,064}} = \sqrt[3]{{{{(0,4)}^3}}} = 0,4.\]

\[\sqrt[3]{{ - 0,216}} = \sqrt[3]{{{{( - 0,6)}^3}}} =  - 0,6.\]

\[\sqrt[3]{{ - 0,008}} = \sqrt[3]{{{{( - 0,2)}^3}}} =  - 0,2.\]