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Question

Làm bài 10 câu từ câu 7 đến câu 15

HT.Phong (9A5) · Accepted Answer

7) $\dfrac{6^{15}\cdot9^{10}}{3^{34}\cdot2^{13}}=\dfrac{2^{15}\cdot3^{15}\cdot\left(3^2\right)^{10}}{3^{34}\cdot2^{13}}=\dfrac{2^{15}\cdot3^{35}}{3^{34}\cdot2^{13}}=2^2\cdot3=12$8) $\dfrac{9^2\cdot2^{11}}{16^2\cdot6^3}=\dfrac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot2^3\cdot3^3}=\dfrac{3^4\cdot2^{11}}{2^{11}\cdot3^3}=3$9) $\dfrac{4^5\cdot9^4}{8^3\cdot27^3}=\dfrac{\left(2^2\right)^5\cdot\left(3^2\right)^4}{\left(2^3\right)^3\cdot\left(3^3\right)^3}=\dfrac{2^{10}\cdot3^8}{2^9\cdot3^9}=\dfrac{2}{3}$10) $\dfrac{27^4\cdot4^3}{9^5\cdot8^2}=\dfrac{\left(3^3\right)^4\cdot\left(2^2\right)^3}{\left(3^2\right)^5\cdot\left(2^3\right)^2}=\dfrac{3^{12}\cdot2^6}{3^{10}\cdot2^6}=3^2=9$11) $\dfrac{3^{29}\cdot4^{16}}{27^9\cdot8^{11}}=\dfrac{3^{29}\cdot\left(2^2\right)^{16}}{\left(3^3\right)^9\cdot\left(2^3\right)^{11}}=\dfrac{3^{29}\cdot2^{32}}{3^{27}\cdot2^{33}}=\dfrac{3^2}{2}=\dfrac{9}{2}$Câu trả lời: 7) $\dfrac{6^{15}\cdot9^{10}}{3^{34}\cdot2^{13}}=\dfrac{2^{15}\cdot3^{15}\cdot\left(3^2\right)^{10}}{3^{34}\cdot2^{13}}=\dfrac{2^{15}\cdot3^{35}}{3^{34}\cdot2^{13}}=2^2\cdot3=12$8) $\dfrac{9^2\cdot2^{11}}{16^2\cdot6^3}=\dfrac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot2^3\cdot3^3}=\dfrac{3^4\cdot2^{11}}{2^{11}\cdot3^3}=3$9) $\dfrac{4^5\cdot9^4}{8^3\cdot27^3}=\dfrac{\left(2^2\right)^5\cdot\left(3^2\right)^4}{\left(2^3\right)^3\cdot\left(3^3\right)^3}=\dfrac{2^{10}\cdot3^8}{2^9\cdot3^9}=\dfrac{2}{3}$10) $\dfrac{27^4\cdot4^3}{9^5\cdot8^2}=\dfrac{\left(3^3\right)^4\cdot\left(2^2\right)^3}{\left(3^2\right)^5\cdot\left(2^3\right)^2}=\dfrac{3^{12}\cdot2^6}{3^{10}\cdot2^6}=3^2=9$11) $\dfrac{3^{29}\cdot4^{16}}{27^9\cdot8^{11}}=\dfrac{3^{29}\cdot\left(2^2\right)^{16}}{\left(3^3\right)^9\cdot\left(2^3\right)^{11}}=\dfrac{3^{29}\cdot2^{32}}{3^{27}\cdot2^{33}}=\dfrac{3^2}{2}=\dfrac{9}{2}$

Toru · Answer

7) $\dfrac{6^{15}.9^{10}}{3^{34}.2^{13}}=\dfrac{\left(2.3\right)^{15}.\left(3^2\right)^{10}}{3^{34}.2^{13}}=\dfrac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}$$=\dfrac{2^{15}.3^{35}}{3^{34}.2^{13}}=2^2.3=12$8) $\dfrac{9^2.2^{11}}{16^2.6^3}=\dfrac{\left(3^2\right)^2.2^{11}}{\left(2^4\right)^2.\left(2.3\right)^3}=\dfrac{3^4.2^{11}}{2^8.2^3.3^3}$$=\dfrac{2^{11}.3^4}{2^{11}.3^3}=3$9) $\dfrac{4^5.9^4}{8^3.27^3}=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4}{\left(2^3\right)^3.\left(3^3\right)^3}=\dfrac{2^{10}.3^8}{2^9.3^9}=\dfrac{2}{3}$10) $\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{\left(3^3\right)^4.\left(2^2\right)^3}{\left(3^2\right)^5.\left(2^3\right)^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=3^2=9$11) $\dfrac{3^{29}.4^{16}}{27^9.8^{11}}=\dfrac{3^{29}.\left(2^2\right)^{16}}{\left(3^3\right)^9.\left(2^3\right)^{11}}=\dfrac{3^{29}.2^{32}}{3^{27}.2^{33}}$$=\dfrac{3^2}{2}=\dfrac{9}{2}$12) $\dfrac{4^{20}.3^{35}}{2^{37}.27^{12}}=\dfrac{\left(2^2\right)^{20}.3^{35}}{2^{37}.\left(3^3\right)^{12}}=\dfrac{2^{40}.3^{35}}{2^{37}.3^{36}}$$=\dfrac{2^3}{3}=\dfrac{8}{3}$13) $\dfrac{6^7.4^2}{9^2.12^5}=\dfrac{\left(2.3\right)^7.\left(2^2\right)^2}{\left(3^2\right)^2.\left(3.2^2\right)^5}=\dfrac{2^7.3^7.2^4}{3^4.3^5.2^{10}}$$=\dfrac{2^{11}.3^7}{2^{10}.3^9}=\dfrac{2}{3^2}=\dfrac{2}{9}$14) $\dfrac{15^2.9^3}{25^3.27^2}=\dfrac{\left(3.5\right)^2.\left(3^2\right)^3}{\left(5^2\right)^3.\left(3^3\right)^2}=\dfrac{3^2.5^2.3^6}{5^6.3^6}$$=\dfrac{3^8.5^2}{5^6.3^6}=\dfrac{3^2}{5^4}=\dfrac{9}{625}$15) $\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(5.2^2\right)^4}{\left(5^2\right)^5.\left(2^2\right)^5}=\dfrac{5^4.5^4.2^8}{5^{10}.2^{10}}$$=\dfrac{5^8.2^8}{5^{10}.2^{10}}=\dfrac{1}{5^2.2^2}=\dfrac{1}{100}$Câu trả lời: 7) $\dfrac{6^{15}.9^{10}}{3^{34}.2^{13}}=\dfrac{\left(2.3\right)^{15}.\left(3^2\right)^{10}}{3^{34}.2^{13}}=\dfrac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}$$=\dfrac{2^{15}.3^{35}}{3^{34}.2^{13}}=2^2.3=12$8) $\dfrac{9^2.2^{11}}{16^2.6^3}=\dfrac{\left(3^2\right)^2.2^{11}}{\left(2^4\right)^2.\left(2.3\right)^3}=\dfrac{3^4.2^{11}}{2^8.2^3.3^3}$$=\dfrac{2^{11}.3^4}{2^{11}.3^3}=3$9) $\dfrac{4^5.9^4}{8^3.27^3}=\dfrac{\left(2^2\right)^5.\left(3^2\right)^4}{\left(2^3\right)^3.\left(3^3\right)^3}=\dfrac{2^{10}.3^8}{2^9.3^9}=\dfrac{2}{3}$10) $\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{\left(3^3\right)^4.\left(2^2\right)^3}{\left(3^2\right)^5.\left(2^3\right)^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=3^2=9$11) $\dfrac{3^{29}.4^{16}}{27^9.8^{11}}=\dfrac{3^{29}.\left(2^2\right)^{16}}{\left(3^3\right)^9.\left(2^3\right)^{11}}=\dfrac{3^{29}.2^{32}}{3^{27}.2^{33}}$$=\dfrac{3^2}{2}=\dfrac{9}{2}$12) $\dfrac{4^{20}.3^{35}}{2^{37}.27^{12}}=\dfrac{\left(2^2\right)^{20}.3^{35}}{2^{37}.\left(3^3\right)^{12}}=\dfrac{2^{40}.3^{35}}{2^{37}.3^{36}}$$=\dfrac{2^3}{3}=\dfrac{8}{3}$13) $\dfrac{6^7.4^2}{9^2.12^5}=\dfrac{\left(2.3\right)^7.\left(2^2\right)^2}{\left(3^2\right)^2.\left(3.2^2\right)^5}=\dfrac{2^7.3^7.2^4}{3^4.3^5.2^{10}}$$=\dfrac{2^{11}.3^7}{2^{10}.3^9}=\dfrac{2}{3^2}=\dfrac{2}{9}$14) $\dfrac{15^2.9^3}{25^3.27^2}=\dfrac{\left(3.5\right)^2.\left(3^2\right)^3}{\left(5^2\right)^3.\left(3^3\right)^2}=\dfrac{3^2.5^2.3^6}{5^6.3^6}$$=\dfrac{3^8.5^2}{5^6.3^6}=\dfrac{3^2}{5^4}=\dfrac{9}{625}$15) $\dfrac{5^4.20^4}{25^5.4^5}=\dfrac{5^4.\left(5.2^2\right)^4}{\left(5^2\right)^5.\left(2^2\right)^5}=\dfrac{5^4.5^4.2^8}{5^{10}.2^{10}}$$=\dfrac{5^8.2^8}{5^{10}.2^{10}}=\dfrac{1}{5^2.2^2}=\dfrac{1}{100}$

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