rút gọn phân số
a)\(\dfrac{2727-101}{3.303+404}\) b)\(\dfrac{8.9-4.15}{12.7-180}\) c)\(\dfrac{-19}{3^2.7.11}\) d)\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
Rút gọn biểu thức: \(A=\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{11}.3^{11}\left(2.3-1\right)}\)
\(=\dfrac{2^{12}.3^{10}\left(1+5\right)}{2^{11}.3^{11}.5}\)
\(=\dfrac{2^{12}.3^{10}.6}{2^{11}.3^{11}.5}=\dfrac{2.6}{3.5}=\dfrac{4}{5}\)
\(A=\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{\left(2^2\right)^6.\left(3^2\right)^5+6^9.6.2^2.5}{\left(2^3\right)^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\dfrac{2^{11}.3^{10}\left(2^1+2^1.5\right)}{2^{11}.3^{10}\left(2^1.3^2-1.3^1\right)}=\dfrac{2+10}{2.9-1.3}=\dfrac{12}{15}=\dfrac{4}{5}\)
Câu 2: Tính
C = \(\dfrac{6^3+3.6^2+3^3}{13}\)
D = \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(C=\dfrac{6^3+3\cdot6^2+3^3}{13}=\dfrac{3^3\cdot8+3^3\cdot4+3^3}{13}=27\)
\(\dfrac{-4^6.9^5-6^9.120}{-8^4.3^{12}-6^{11}}\)
\(=\dfrac{-2^{12}\cdot3^{10}-2^{12}\cdot3^{10}\cdot5}{-2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot7}=\dfrac{2\cdot6}{3\cdot7}=\dfrac{12}{21}=\dfrac{4}{7}\)
\(\dfrac{10^3+2.5^3+5^3}{55}-\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{5^3\left(2^3+2+1\right)}{55}-\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=5^2-\dfrac{2^{12}\cdot3^{10}\cdot\left(1+5\right)}{2^{11}\cdot3^{11}\left(2\cdot3-1\right)}=25-\dfrac{2}{3}\cdot\dfrac{6}{5}\)
=25-4/5
=24,2
Rút gọn rồi quy đồng mẫu các phân số sau :
a)\(\frac{5.6+5.7}{5.8+20}\)và\(\frac{8.9-4.15}{12.7-180}\)
b)\(\frac{-5^2-5.3^2}{5^3+5^2.3^2}\)và \(\frac{4^6.9^5+69.120}{8^4.3^{12}-6^{11}}\)
\(a,\frac{5\cdot6+5\cdot7}{5\cdot8+20}=\frac{\left(5\cdot6+5\cdot7\right)\div2}{\left(5.8+20\right)\div2}=\frac{13}{12}\)
\(\frac{8.9-4.15}{12.7-180}=\frac{12.6-12.5}{12.7-12.15}=\frac{1}{-8}=\frac{-1}{8}\)
\(Ta\)\(co\)\(\frac{13}{12}=\frac{13.2}{12.2}=\frac{26}{24}\)
\(\frac{-1}{8}=\frac{3\left(-1\right)}{3.8}=\frac{-3}{24}\)
Phần b bạn tính ra rồi làm tương tự phần a nha chúc bạn học giỏi!!!
Cho 3 phân số:
\(\frac{-5^2-5.3^2}{5^3+5^2.3^2};\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}};\frac{2929-101}{2.1919+404}\)
Rút gọn rồi quy đòng 3 ps trên
\(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}+2^9\cdot2^3\cdot3^9\cdot3\cdot5}{2^{12}\cdot3^{12}-2^{11}\cdot3^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}+2^{12}\cdot3^{10}\cdot5}{2^{11}\cdot3^{11}\cdot5}\)
\(=\dfrac{2^{12}\cdot3^{10}\cdot6}{2^{11}\cdot3^{11}\cdot5}=\dfrac{2\cdot6}{3\cdot5}=\dfrac{12}{15}=\dfrac{4}{5}\)
\(\dfrac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}\)
ta có : \(\dfrac{4^6.9^5+6^9.120}{-8^4.3^{12}-6^{11}}=\dfrac{4\left(4^5.9^5+5.6^{10}\right)}{-2^{12}.3^{12}-6^{11}}=\dfrac{4\left(2^{10}.3^{10}+5.6^{10}\right)}{-2^{12}.3^{12}-6^{11}}\)
\(=\dfrac{4\left(6^{10}+5.6^{10}\right)}{-6^{12}-6^{11}}=\dfrac{4.6^{11}}{-6^{11}\left(6+1\right)}=-\dfrac{4}{7}\)
\(\dfrac{4^6.9^5+6^9.120}{-8^4.3^{12}+6^{11}}\)
\(=\dfrac{2^{12}\cdot3^{10}+2^9\cdot3^9\cdot2^3\cdot3\cdot5}{-2^{12}\cdot3^{12}+2^{11}\cdot3^{11}}\)
\(=-\dfrac{2^{12}\cdot3^{10}\left(1+5\right)}{2^{11}\cdot3^{11}\cdot\left(2\cdot3-1\right)}=\dfrac{-2}{3}\)