1. The problem states to simplify $4.) (10ab)^{3/8}$ and expresses a root form. 2. The given expression is $(10ab)^{3/8}$. 3. Recall that an exponent in fraction form $\frac{m}{n}$ means the $n$th root of the base raised to the $m$th power: $a^{m/n} = \sqrt[n]{a^m}$. 4. Applying this to $(10ab)^{3/8}$: $$ (10ab)^{3/8} = \sqrt[8]{(10ab)^3} $$ 5. Use the property of exponents distributing over multiplication inside the root: $$ \sqrt[8]{10^3 \cdot a^3 \cdot b^3} $$ 6. This gives the simplified radical expression: $$ \sqrt[8]{10^3 a^3 b^3} $$ 7. Thus, the simplified expression is $\boxed{\sqrt[8]{10^3 a^3 b^3}}$ or equivalently $(10ab)^{3/8}$ as given.