1. **State the problem:** Simplify the expression $$\frac{2np^5r^7}{16p^{20}r}$$ without negative exponents. 2. **Write the formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{2}{16} = \frac{\cancel{2} \times 1}{\cancel{2} \times 8} = \frac{1}{8}$$. 4. **Simplify the powers of $p$:** $$p^{5} \div p^{20} = p^{5-20} = p^{-15}$$. 5. **Simplify the powers of $r$:** $$r^{7} \div r^{1} = r^{7-1} = r^{6}$$. 6. **Combine all parts:** $$\frac{n p^{5} r^{7}}{16 p^{20} r} = \frac{1}{8} n p^{-15} r^{6}$$. 7. **Remove negative exponents:** $$p^{-15} = \frac{1}{p^{15}}$$, so $$\frac{1}{8} n p^{-15} r^{6} = \frac{n r^{6}}{8 p^{15}}$$. **Final answer:** $$\boxed{\frac{n r^{6}}{8 p^{15}}}$$