1. **State the problem:** Simplify the expression $$\left( \frac{-2b^2}{a} \right)^4$$ and write the answer without parentheses. 2. **Recall the power of a quotient rule:** $$\left( \frac{x}{y} \right)^n = \frac{x^n}{y^n}$$ and the power of a product rule: $$ (xy)^n = x^n y^n $$. 3. **Apply the power to numerator and denominator:** $$\left( \frac{-2b^2}{a} \right)^4 = \frac{(-2b^2)^4}{a^4}$$ 4. **Simplify the numerator:** $$(-2b^2)^4 = (-2)^4 (b^2)^4 = 16 b^{8}$$ 5. **Write the full simplified expression:** $$\frac{16 b^{8}}{a^{4}}$$ 6. **Final answer without parentheses:** $$\frac{16 b^{8}}{a^{4}}$$