1. **State the problem:** Simplify the expression $$\left(-3a^5 / b^4\right)^6$$. 2. **Recall the power of a quotient rule:** When raising a quotient to a power, apply the exponent to both numerator and denominator: $$\left(\frac{x}{y}\right)^n = \frac{x^n}{y^n}$$. 3. **Apply the power to each part:** $$\left(-3a^5\right)^6 = (-3)^6 \cdot (a^5)^6$$ $$\left(b^4\right)^6 = b^{4 \cdot 6} = b^{24}$$ 4. **Calculate powers:** $$(-3)^6 = (-3) \times (-3) \times (-3) \times (-3) \times (-3) \times (-3) = 729$$ $$ (a^5)^6 = a^{5 \times 6} = a^{30}$$ 5. **Combine numerator and denominator:** $$\frac{729 a^{30}}{b^{24}}$$ 6. **Final simplified expression:** $$\boxed{\frac{729 a^{30}}{b^{24}}}$$ Note: The original expression raised to the 6th power results in a positive value because an even power eliminates the negative sign.