1. **State the problem:** Simplify the expression $$\left(\frac{-7a}{b^{3}}\right)^2$$ without parentheses. 2. **Recall the rule:** When raising a fraction to a power, raise both numerator and denominator to that power: $$\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$$ 3. **Apply the power to numerator and denominator:** $$\left(\frac{-7a}{b^{3}}\right)^2 = \frac{(-7a)^2}{(b^3)^2}$$ 4. **Simplify numerator:** $$(-7a)^2 = (-7)^2 \cdot a^2 = 49a^2$$ 5. **Simplify denominator:** $$(b^3)^2 = b^{3 \times 2} = b^6$$ 6. **Combine results:** $$\frac{49a^2}{b^6}$$ 7. **Final answer:** $$\frac{49a^2}{b^6}$$