1. **State the problem:** Calculate the value of $$5^{-4} \div \left(3^{3} \div 5^{7}\right)$$. 2. **Recall the rules:** - Division of exponents with the same base: $$a^{m} \div a^{n} = a^{m-n}$$. - Division of fractions: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$. 3. **Rewrite the expression:** $$5^{-4} \div \left(\frac{3^{3}}{5^{7}}\right) = 5^{-4} \times \frac{5^{7}}{3^{3}}$$ 4. **Multiply the powers of 5:** $$5^{-4} \times 5^{7} = 5^{-4+7} = 5^{3}$$ 5. **Calculate the powers:** $$5^{3} = 125$$ $$3^{3} = 27$$ 6. **Combine the results:** $$\frac{125}{27}$$ **Final answer:** $$\frac{125}{27}$$