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Gợi ý : Phân tích hết ra thành tích các thừa số nguyên tố rồi đặt cái chung ra ngoài
-> rút gọn
-> kết quả
P/S : bài này cx ko dài lắm nhưg lười ^^
\(B=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^6}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^5.\left(1-3\right)}{2^{12}.3^6.\left(3+1\right)}-\frac{5^9.7^3.\left(1-7\right)}{5^9.7^3\left(1+2^3.1\right)}\)
\(=\frac{-1}{2}-\frac{-2}{3}=\frac{-7}{6}\)
\(B=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{16}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{16}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.\left(2.7\right)^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{16}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^4.\left(3-1\right)}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3\left(5^6-7\right)}{5^9.7^3.\left(1+2^3\right)}\)
\(=\frac{2}{3.4}-\frac{5.\left(15625-7\right)}{1+8}\)
\(=\frac{1}{6}-\frac{\text{78090}}{9}\)
đề ghi vậy , ko ra kq nhé
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{2^{12}.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3.7\right)^3+5^9.2^3.7^3}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}=\frac{2^{12}.3^4\left(3-1\right)}{2^{12}.3^5\left(3+1\right)}-\frac{5^{10}.7^3\left(1-7\right)}{5^9.7^3\left(1+2^3\right)}=\frac{2}{3.4}-\frac{5.\left(-6\right)}{9}\)
\(=\frac{1}{6}-\frac{-10}{3}=\frac{1}{6}-\frac{-20}{6}=\frac{21}{6}=\frac{7}{2}\)
Lẽ ra là làm xong cho bạn rồi, vậy mà tự nhiên máy sập, giờ chép lại, oải quá :|
\(\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
Phân tích từ số:
\(\frac{2^{12}.3^5-4^2.4^4.3^4}{2^{12}.3.3^5+4^2.4^4.3.3^4}=\frac{1}{6}\)
\(\frac{5^9.5.7^3-5^9.5.7^3.7}{5^9.7^3+5^9.2^3.7^3}=\frac{-10}{3}\)
Sau khi rút gọn là:
\(\frac{1}{6}-\left(-\frac{10}{3}\right)=\frac{1}{6}+\frac{10}{3}=\frac{7}{2}\)
TA có\(\frac{2^{12}.3^5.4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3}\)
=\(\frac{2^{12}.3^5.2^{12}.3^4}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3}\)
=\(\frac{2^{24}.3^9}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7\right)}{5^9.7^3}\)
=\(2^{20}.3^4-30\)
c: \(C=\dfrac{\left(\dfrac{2}{5}\cdot5\right)^7+\dfrac{9^3}{4^3}:\dfrac{3^3}{16^3}}{2^7\cdot5^2+2^9}=\dfrac{1+1728}{3712}=\dfrac{1729}{3712}\)
\(D=\dfrac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}=\dfrac{3^5-3^4}{3^6+3^5}=\dfrac{3^4\left(3-1\right)}{3^5\left(3+1\right)}=\dfrac{2}{3\cdot4}=\dfrac{2}{12}=\dfrac{1}{6}\)
\(E=\dfrac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}=\dfrac{5^{10}\cdot7^3\cdot\left(-6\right)}{5^9\cdot7^3\cdot9}=5\cdot\dfrac{-2}{3}=\dfrac{-10}{3}\)