1. Simplify $a^{-3}$ using the rule $x^{-n} = \frac{1}{x^n}$: $$a^{-3} = \frac{1}{a^3}$$ 2. Simplify $3x^0$ using the rule $x^0 = 1$ for any $x \neq 0$: $$3x^0 = 3 \times 1 = 3$$ 3. Simplify $m^5 n^0$ using $n^0 = 1$: $$m^5 n^0 = m^5 \times 1 = m^5$$ 4. Simplify $(4a^2)^0$ using the rule $(x)^0 = 1$ for any $x \neq 0$: $$(4a^2)^0 = 1$$ 5. Simplify $2m^{-1}$ using $m^{-1} = \frac{1}{m}$: $$2m^{-1} = 2 \times \frac{1}{m} = \frac{2}{m}$$ 6. Simplify $(xy)^{-3}$ using $(xy)^{-n} = \frac{1}{(xy)^n}$: $$(xy)^{-3} = \frac{1}{(xy)^3} = \frac{1}{x^3 y^3}$$ 7. Simplify $(2a)^{-3}$ using $(xy)^{-n} = \frac{1}{(xy)^n}$: $$(2a)^{-3} = \frac{1}{(2a)^3} = \frac{1}{8a^3}$$ 8. Simplify $-5y^{-2}$ using $y^{-2} = \frac{1}{y^2}$: $$-5y^{-2} = -5 \times \frac{1}{y^2} = -\frac{5}{y^2}$$ 9. Simplify $\frac{a^{-3}}{b}$ using $a^{-3} = \frac{1}{a^3}$: $$\frac{a^{-3}}{b} = \frac{\frac{1}{a^3}}{b} = \frac{1}{a^3 b}$$ 10. Simplify $\frac{x^{-5}}{y^{-3}}$ using $x^{-5} = \frac{1}{x^5}$ and $y^{-3} = \frac{1}{y^3}$: $$\frac{x^{-5}}{y^{-3}} = \frac{\frac{1}{x^5}}{\frac{1}{y^3}} = \frac{1}{x^5} \times y^3 = \frac{y^3}{x^5}$$