1. Simplify $\frac{10^{15}}{10^3}$ using the quotient rule for exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ $$\frac{10^{15}}{10^3} = 10^{15-3} = 10^{12}$$ 2. Simplify $\frac{(-3)^4}{(-3)^{-3}}$: $$\frac{(-3)^4}{(-3)^{-3}} = (-3)^{4 - (-3)} = (-3)^{4+3} = (-3)^7$$ 3. Simplify $\frac{8}{8^3}$: $$\frac{8}{8^3} = 8^{1-3} = 8^{-2} = \frac{1}{8^2}$$ 4. Simplify $\frac{a^{12}}{a^2}$: $$\frac{a^{12}}{a^2} = a^{12-2} = a^{10}$$ 5. Simplify $\frac{m^{-2} n^{16}}{m^4 n^2}$: $$= m^{-2-4} n^{16-2} = m^{-6} n^{14} = \frac{n^{14}}{m^6}$$ 6. Simplify $\frac{p^5 q^{-10}}{p^6 q^{-2}}$: $$= p^{5-6} q^{-10 - (-2)} = p^{-1} q^{-8} = \frac{1}{p q^8}$$ 7. Simplify $\frac{63 x^{18}}{9 x^2}$: Divide coefficients: $\frac{63}{9} = 7$ Subtract exponents: $x^{18-2} = x^{16}$ Answer: $7 x^{16}$ 8. Simplify $\frac{28 r^4}{-7 r^{15}}$: Divide coefficients: $\frac{28}{-7} = -4$ Subtract exponents: $r^{4-15} = r^{-11} = \frac{1}{r^{11}}$ Answer: $-4 \frac{1}{r^{11}} = -\frac{4}{r^{11}}$ 9. Simplify $\frac{-16 a^9}{8 a^4}$: Divide coefficients: $\frac{-16}{8} = -2$ Subtract exponents: $a^{9-4} = a^5$ Answer: $-2 a^5$ 10. Simplify $\frac{5 p^{-7}}{20 p^2}$: Divide coefficients: $\frac{5}{20} = \frac{1}{4}$ Subtract exponents: $p^{-7 - 2} = p^{-9} = \frac{1}{p^9}$ Answer: $\frac{1}{4 p^9}$ 11. Simplify $\frac{16 n^{-3}}{24 n^{-10}}$: Divide coefficients: $\frac{16}{24} = \frac{2}{3}$ Subtract exponents: $n^{-3 - (-10)} = n^{7}$ Answer: $\frac{2}{3} n^{7}$ 12. Simplify $\frac{15 x^2 y^2}{12 x^3 y^?}$ (assuming the exponent on $y$ is missing, so cannot simplify fully). If the exponent is $m$, then: $$\frac{15 x^2 y^2}{12 x^3 y^m} = \frac{15}{12} x^{2-3} y^{2 - m} = \frac{5}{4} x^{-1} y^{2 - m} = \frac{5 y^{2 - m}}{4 x}$$ If you provide the exponent for $y$, I can complete this step. Final answers with positive exponents: 1. $10^{12}$ 2. $(-3)^7$ 3. $\frac{1}{8^2}$ 4. $a^{10}$ 5. $\frac{n^{14}}{m^6}$ 6. $\frac{1}{p q^8}$ 7. $7 x^{16}$ 8. $-\frac{4}{r^{11}}$ 9. $-2 a^5$ 10. $\frac{1}{4 p^9}$ 11. $\frac{2}{3} n^{7}$ 12. $\frac{5 y^{2 - m}}{4 x}$ (pending $y$ exponent)