1. **State the problem:** Simplify the expression $$(-5x^5 y^3)^3$$. 2. **Recall the power of a power rule:** When raising a power to another power, multiply the exponents: $$\left(a^m\right)^n = a^{m \times n}$$. 3. **Apply the rule to each factor inside the parentheses:** - For the constant: $$(-5)^3$$ - For $$x^5$$: $$\left(x^5\right)^3 = x^{5 \times 3} = x^{15}$$ - For $$y^3$$: $$\left(y^3\right)^3 = y^{3 \times 3} = y^9$$ 4. **Calculate the constant:** $$(-5)^3 = -125$$. 5. **Combine all parts:** $$(-5x^5 y^3)^3 = -125 x^{15} y^9$$. 6. **Final answer:** $$\boxed{-125 x^{15} y^9}$$