Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 78: 39

$-\sqrt[3]{2}$

Using the properties of radicals that we know, we simplify: $\displaystyle 5\sqrt[3]{2}-2\sqrt[3]{54}=5\sqrt[3]{2}-2\sqrt[3]{27*2}=5\sqrt[3]{2}-2\sqrt[3]{3^3*2}=5\sqrt[3]{2}-2*3\sqrt[3]{2}=5\sqrt[3]{2}-6\sqrt[3]{2}=-\sqrt[3]{2}$