1. Simplify $\frac{10^{15}}{10^3}$ using the rule $\frac{a^m}{a^n} = a^{m-n}$. $$\frac{10^{15}}{10^3} = 10^{15-3} = 10^{12}$$ 2. Simplify $\frac{(-3)^4}{(-3)^{-3}}$ using the same exponent subtraction rule. $$\frac{(-3)^4}{(-3)^{-3}} = (-3)^{4 - (-3)} = (-3)^7$$ 3. Simplify $\frac{8}{8^3}$. Rewrite numerator as $8^1$: $$\frac{8^1}{8^3} = 8^{1-3} = 8^{-2} = \frac{1}{8^2}$$ 4. Simplify $\frac{a^{12}}{a^2}$. $$\frac{a^{12}}{a^2} = a^{12-2} = a^{10}$$ 5. Simplify $\frac{m^{-2} n^{16}}{m^4 n^2}$. Apply exponent subtraction for each variable: $$\frac{m^{-2}}{m^4} = m^{-2-4} = m^{-6}$$ $$\frac{n^{16}}{n^2} = n^{16-2} = n^{14}$$ Combine: $$m^{-6} n^{14} = \frac{n^{14}}{m^6} = \frac{1}{m^6 n^{-14}}$$ but since $n^{14}$ is positive exponent, final is: $$\frac{1}{m^6 n^{14}}$$ 6. Simplify $\frac{p^5 q^{-10}}{p^6 q^{-2}}$. $$p^{5-6} = p^{-1}$$ $$q^{-10 - (-2)} = q^{-10 + 2} = q^{-8}$$ Combine: $$p^{-1} q^{-8} = \frac{1}{p q^8}$$ 7. Simplify $\frac{7x^{18}}{x^2}$. $$7 \times x^{18-2} = 7x^{16}$$ 8. Simplify $\frac{28 r^4}{-7 r^{15}}$. Divide coefficients: $$\frac{28}{-7} = -4$$ Subtract exponents: $$r^{4-15} = r^{-11}$$ Combine: $$-4 r^{-11} = -\frac{4}{r^{11}}$$ 9. Simplify $\frac{-16 a^9}{8 a^{-4}}$. Divide coefficients: $$\frac{-16}{8} = -2$$ Subtract exponents: $$a^{9 - (-4)} = a^{9+4} = a^{13}$$ Combine: $$-2 a^{13}$$ 10. Simplify $\frac{1}{9 p^7 q^2}$. Already simplified with positive exponents. 11. Simplify $\frac{16 w^{-3}}{24 w^{-10}}$. Divide coefficients: $$\frac{16}{24} = \frac{2}{3}$$ Subtract exponents: $$w^{-3 - (-10)} = w^{-3 + 10} = w^7$$ Combine: $$\frac{2}{3} w^7$$ 12. Simplify $\frac{15 x^2 y^2}{12 x^3 y^1}$. Divide coefficients: $$\frac{15}{12} = \frac{5}{4}$$ Subtract exponents: $$x^{2-3} = x^{-1} = \frac{1}{x}$$ $$y^{2-1} = y^1 = y$$ Combine: $$\frac{5}{4} \times \frac{y}{x} = \frac{5y}{4x}$$