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