1. Simplify $\frac{8^8}{8^4}$. Use the rule $\frac{a^m}{a^n} = a^{m-n}$. $$\frac{8^8}{8^4} = 8^{8-4} = 8^4$$ 2. Simplify $\frac{a^4 b^6}{a b^3}$. Apply $\frac{a^m}{a^n} = a^{m-n}$ and $\frac{b^m}{b^n} = b^{m-n}$. $$\frac{a^4 b^6}{a b^3} = a^{4-1} b^{6-3} = a^3 b^3$$ 3. Simplify $\frac{xy^2}{xy}$. $$\frac{xy^2}{xy} = x^{1-1} y^{2-1} = y$$ 4. Simplify $\frac{m^5 n p}{m^4 p}$. $$\frac{m^5 n p}{m^4 p} = m^{5-4} n^{1} p^{1-1} = m n$$ 5. Simplify $\frac{5 c^2 d^3}{-4 c^2 d}$. $$\frac{5 c^2 d^3}{-4 c^2 d} = \frac{5}{-4} c^{2-2} d^{3-1} = -\frac{5}{4} d^2$$ 6. Simplify $\frac{8 y^7 z^6}{4 y^6 z^5}$. $$\frac{8 y^7 z^6}{4 y^6 z^5} = 2 y^{7-6} z^{6-5} = 2 y z$$ 7. Simplify $\left(\frac{x^{1/3} g}{3 h^6}\right)^3$. Apply power to numerator and denominator: $$\frac{(x^{1/3})^3 g^3}{3^3 (h^6)^3} = \frac{x^{1} g^3}{27 h^{18}} = \frac{x g^3}{27 h^{18}}$$ 8. Simplify $\left(\frac{6 w^5}{7 p^6 r^3}\right)^2$. $$\frac{6^2 w^{10}}{7^2 p^{12} r^{6}} = \frac{36 w^{10}}{49 p^{12} r^{6}}$$ 9. Simplify $\frac{-4 x^2}{24 x^5}$. $$\frac{-4}{24} x^{2-5} = -\frac{1}{6} x^{-3} = -\frac{1}{6 x^3}$$ 10. Simplify $x^3 y^{-5} x^{-8}$. $$x^{3-8} y^{-5} = x^{-5} y^{-5} = \frac{1}{x^5 y^5}$$ 11. Simplify $p q^{-2} r^{-3}$. $$p q^{-2} r^{-3} = \frac{p}{q^2 r^3}$$ 12. Simplify $12^{-2}$. $$12^{-2} = \frac{1}{12^2} = \frac{1}{144}$$ 13. Simplify $\left(\frac{3}{7}\right)^{-2}$. $$\left(\frac{3}{7}\right)^{-2} = \left(\frac{7}{3}\right)^2 = \frac{49}{9}$$ 14. Simplify $\left(\frac{4}{3}\right)^{-4}$. $$\left(\frac{4}{3}\right)^{-4} = \left(\frac{3}{4}\right)^4 = \frac{81}{256}$$ 15. Simplify $\frac{22 r^3 s^2}{11 r^2 s^{-3}}$. $$\frac{22}{11} r^{3-2} s^{2-(-3)} = 2 r s^{5}$$ 16. Simplify $\frac{-15 w^0 u^{-1}}{5 u^3}$. $$\frac{-15}{5} w^0 u^{-1-3} = -3 u^{-4} = -\frac{3}{u^4}$$ 17. Simplify $\frac{8 c^3 d^2 f^4}{4 c^{-1} d^2 f^{-3}}$. $$\frac{8}{4} c^{3-(-1)} d^{2-2} f^{4-(-3)} = 2 c^{4} f^{7}$$ 18. Simplify $\left(\frac{x^{-3} y^{5}}{4^{-3}}\right)^0$. Any nonzero expression to the zero power is 1: $$1$$