1. El problema consiste en realizar varias operaciones de división y multiplicación con números en notación científica. 2. Recordemos la regla básica para dividir potencias con base 10: $$\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}$$ 3. Regla para multiplicar potencias con base 10: $$(a \times 10^m) \times (b \times 10^n) = (a \times b) \times 10^{m+n}$$ 4. Ahora resolvemos cada operación paso a paso: - $$\frac{3.6 \times 10^2}{6 \times 10^3} = \frac{3.6}{6} \times 10^{2-3} = 0.6 \times 10^{-1} = 6 \times 10^{-2}$$ - $$\frac{9 \times 10^3}{5 \times 10^3} = \frac{9}{5} \times 10^{3-3} = 1.8 \times 10^0 = 1.8$$ - $$\frac{9 \times 10^8}{3 \times 10^9} = \frac{9}{3} \times 10^{8-9} = 3 \times 10^{-1} = 0.3$$ - $$\frac{9 \times 10^{13}}{7 \times 10^7} = \frac{9}{7} \times 10^{13-7} = 1.2857 \times 10^6$$ (aproximado) - $$\frac{6 \times 10^9}{9 \times 10^{-3}} = \frac{6}{9} \times 10^{9 - (-3)} = 0.6667 \times 10^{12} = 6.667 \times 10^{11}$$ - $$(2 \times 10^{-2}) \times (5 \times 10^{-3}) = (2 \times 5) \times 10^{-2 + (-3)} = 10 \times 10^{-5} = 1 \times 10^{-4}$$ - $$\frac{4 \times 10^{-2}}{5 \times 10^3} = \frac{4}{5} \times 10^{-2-3} = 0.8 \times 10^{-5} = 8 \times 10^{-6}$$ - $$\frac{8 \times 10^5}{2 \times 10^7} = \frac{8}{2} \times 10^{5-7} = 4 \times 10^{-2}$$ - $$7 \times 10^5 \times 17 \times 10^9 = (7 \times 17) \times 10^{5+9} = 119 \times 10^{14} = 1.19 \times 10^{16}$$ - $$\frac{4 \times 10^7}{12 \times 10^3} = \frac{4}{12} \times 10^{7-3} = 0.3333 \times 10^{4} = 3.333 \times 10^3$$ - $$\frac{8 \times 10^7}{19 \times 10^3} = \frac{8}{19} \times 10^{7-3} = 0.421 \times 10^{4} = 4.21 \times 10^3$$ - $$\frac{2.7 \times 10^7}{19 \times 10^3} = \frac{2.7}{19} \times 10^{7-3} = 0.1421 \times 10^4 = 1.421 \times 10^3$$ - $$(9 \times 10^{11}) \times (3 \times 10^9) = (9 \times 3) \times 10^{11+9} = 27 \times 10^{20} = 2.7 \times 10^{21}$$ - $$(2.1 \times 10^7) \times (5 \times 10^8) = (2.1 \times 5) \times 10^{7+8} = 10.5 \times 10^{15} = 1.05 \times 10^{16}$$ - $$(3 \times 10^5) \times (8 \times 10^3) = (3 \times 8) \times 10^{5+3} = 24 \times 10^{8} = 2.4 \times 10^{9}$$ - $$\frac{5.5 \times 10^4}{1.1 \times 10^2} = \frac{5.5}{1.1} \times 10^{4-2} = 5 \times 10^{2}$$ - $$\frac{4.2 \times 10^{-9}}{3 \times 10^{-3}} = \frac{4.2}{3} \times 10^{-9 - (-3)} = 1.4 \times 10^{-6}$$ - $$\frac{9.6 \times 10^6}{8 \times 10^3} = \frac{9.6}{8} \times 10^{6-3} = 1.2 \times 10^{3}$$ 5. Resumen de algunas respuestas en notación científica: - $$6 \times 10^{-2}$$ - $$1.8$$ - $$0.3$$ - $$1.29 \times 10^6$$ (aprox) - $$6.667 \times 10^{11}$$ - $$1 \times 10^{-4}$$ - $$8 \times 10^{-6}$$ - $$4 \times 10^{-2}$$ - $$1.19 \times 10^{16}$$ - $$3.33 \times 10^{3}$$ - $$4.21 \times 10^{3}$$ - $$1.42 \times 10^{3}$$ - $$2.7 \times 10^{21}$$ - $$1.05 \times 10^{16}$$ - $$2.4 \times 10^{9}$$ - $$5 \times 10^{2}$$ - $$1.4 \times 10^{-6}$$ - $$1.2 \times 10^{3}$$