Chapter 12 - Exponential Functions and Logarithmic Functions - 12.1 Composite Functions and Inverse Functions - 12.1 Exercise Set - Page 788: 78

$2ab^{4}\cdot\sqrt[3]{5a^{2}}$

Apply the rules: $x^{m+n}=x^{m}x^{n}$ and $(x^{m})^{n}=x^{mn}$ $=\sqrt[3]{8\cdot 5\cdot a^{3}\cdot a^{2}\cdot(b^{4})^{3}}$ $=\sqrt[3]{2^{3}\cdot a^{3}\cdot(b^{4})^{3}\cdot 5\cdot a^{2}}$ $=\sqrt[3]{2^{3}\cdot a^{3}\cdot(b^{4})^{3}}\cdot\sqrt[3]{5\cdot a^{2}}$ $=2ab^{4}\cdot\sqrt[3]{5a^{2}}$