a: \(\frac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54}\cdot\sqrt[3]{4}\)
\(=\sqrt[3]{27}-\sqrt[3]{216}\)
=3-6
=-3
b: \(\left(\sqrt[3]{25}-\sqrt[3]{10}+\sqrt[3]{4}\right)\left(\sqrt[3]{5}+\sqrt[3]{2}\right)\)
\(=\left(\sqrt[3]{5}+\sqrt[3]{2}\right)\left\lbrack\left(\sqrt[3]{5}\right)^2-\sqrt[3]{5}\cdot\sqrt[3]{2}+\left(\sqrt[3]{2}\right)^2\right\rbrack\)
\(=\left(\sqrt[3]{5}\right)^3+\left(\sqrt[3]{2}\right)^3\)
=5+2=7
c: \(\sqrt[3]{-64}-\sqrt[3]{125}+\sqrt[3]{216}\)
=-4-5+6
=-9+6
=-3
d: \(\left(\sqrt[3]{4}+1\right)^3-\left(\sqrt[3]{4}-1\right)^3\)
\(=\left(4+3\cdot\sqrt[3]{16}+3\sqrt[3]{4}+1\right)-\left(4-3\cdot\sqrt[3]{16}+3\cdot\sqrt[3]{4}-1\right)=6\cdot\sqrt[3]{16}+2=12\sqrt[3]{2}+2\)
