1. The problem is to find the fourth root of 0.0016, which means we want to find a number $x$ such that $$x^4 = 0.0016.$$ 2. Recall the definition of the fourth root: $$\sqrt[4]{a} = a^{\frac{1}{4}}.$$ So we can rewrite the problem as $$x = 0.0016^{\frac{1}{4}}.$$ 3. Convert 0.0016 to a fraction or a power of 10 for easier calculation: $$0.0016 = \frac{16}{10000} = \frac{16}{10^4} = 16 \times 10^{-4}.$$ 4. Now apply the fourth root to each factor: $$x = \sqrt[4]{16 \times 10^{-4}} = \sqrt[4]{16} \times \sqrt[4]{10^{-4}}.$$ 5. Calculate each root separately: $$\sqrt[4]{16} = 2$$ because $2^4 = 16$, and $$\sqrt[4]{10^{-4}} = 10^{-1} = 0.1$$ because $(10^{-1})^4 = 10^{-4}.$ 6. Multiply the results: $$x = 2 \times 0.1 = 0.2.$$ Therefore, the fourth root of 0.0016 is $$\boxed{0.2}.$$