1. Stating the problem: Simplify the expression $$a^{-7} b^{2} c^{-1} = \frac{2 n^{-5} p^{0}}{m^{-2}}$$. 2. Recall the rules of exponents: - $x^{-n} = \frac{1}{x^n}$ - $x^0 = 1$ - When dividing powers with the same base, subtract exponents. 3. Simplify the right side: Since $p^0 = 1$, the expression becomes $$\frac{2 n^{-5}}{m^{-2}}$$. 4. Rewrite negative exponents as fractions: $$2 \times \frac{1}{n^5} \times m^{2} = 2 m^{2} n^{-5}$$. 5. The original expression is an equation, so it states: $$a^{-7} b^{2} c^{-1} = 2 m^{2} n^{-5}$$. 6. If the goal is to write both sides with positive exponents: Left side: $$\frac{b^{2}}{a^{7} c}$$ Right side: $$2 m^{2} \frac{1}{n^{5}} = \frac{2 m^{2}}{n^{5}}$$. Final simplified form: $$\frac{b^{2}}{a^{7} c} = \frac{2 m^{2}}{n^{5}}$$.