1. **State the problem:** Simplify the expression $$\left(\frac{-9y}{x^3}\right)^2$$ without parentheses. 2. **Recall the power rule for quotients:** When raising a quotient to a power, raise both numerator and denominator to that power: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ 3. **Apply the power to numerator and denominator:** $$\left(\frac{-9y}{x^3}\right)^2 = \frac{(-9y)^2}{(x^3)^2}$$ 4. **Simplify numerator:** $$(-9y)^2 = (-9)^2 \cdot y^2 = 81y^2$$ 5. **Simplify denominator:** $$ (x^3)^2 = x^{3 \times 2} = x^6$$ 6. **Write the simplified expression:** $$\frac{81y^2}{x^6}$$ This is the expression without parentheses and fully simplified.