Câu hỏi của Nguyễn Mạnh Hùng

Question

tính $\dfrac{^{7.12^8.5^4-6^9.20^4}}{6^{10}.10^5-7.3^9.80^4}$

Hoàng Thị Ngọc Anh · Accepted Answer

Ta có: $\dfrac{7.12^8.5^4-6^9.20^4}{6^{10}.10^5-7.3^9.80^4}$

$=\dfrac{7.3^8.2^{16}.5^4-2^9.3^9.5^4.2^8}{2^{10}.3^{10}.2^5.5^5-7.3^9.2^{15}.2.5^4}$

$=\dfrac{2^{16}.5^4.3^8\left(7-2.3\right)}{2^{15}.3^9.5^4\left(15-7.2\right)}$

$=\dfrac{2^{15}.5^4.3^8.2}{2^{15}.3^8.3.5^4}$

$=\dfrac{2}{3}$.Câu trả lời: Ta có: $\dfrac{7.12^8.5^4-6^9.20^4}{6^{10}.10^5-7.3^9.80^4}$

$=\dfrac{7.3^8.2^{16}.5^4-2^9.3^9.5^4.2^8}{2^{10}.3^{10}.2^5.5^5-7.3^9.2^{15}.2.5^4}$

$=\dfrac{2^{16}.5^4.3^8\left(7-2.3\right)}{2^{15}.3^9.5^4\left(15-7.2\right)}$

$=\dfrac{2^{15}.5^4.3^8.2}{2^{15}.3^8.3.5^4}$

$=\dfrac{2}{3}$.