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a) \(A=\frac{6^3.9^7.4^3-16^2.81^4}{\left(24.3\right)^2}\)
\(A=\frac{2^3.3^3.3^{14}.2^6-2^8.3^{16}}{24^2.3^2}\)
\(A=\frac{2^9.3^{17}-2^8.3^{16}}{3^2.8^2.3^2}\)
\(A=\frac{2^8.3^{16}.\left(2.3-1\right)}{3^4.2^6}\)
\(A=\frac{2^8.3^{16}.5}{3^4.2^6}=2.3^{12}.5=10.3^{12}\)
b) \(B=2198+123-198-1123+42\)
\(B=\left(2198-198\right)+\left(123-1123\right)+42\)
\(B=2000-1000+42=1042\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{1}{2}-\frac{1}{3}-\frac{1}{6}\right)\text{ }\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right)\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)\)
\(Q=\left(\frac{1}{99}+\frac{12}{999}+\frac{123}{999}\right).0\)
\(Q=0\)
Q=(1/99+12/999+123/999).(1/2-1/3-1/6) =(1/99+12/999+123/999).0 Q=0
Để A có giá trị nguyên hay A \(\in\)Z thì ( 3 - n ) \(\in\)Ư(4) .
Mà : Ư(4) = { 1 ; 2 ; 4 ; -1 ; - 2 ; -4 }
Nếu : 3 - n = 1 => n = 2
3 - n = 2 => n = 1
3 - n = 4 => n = -1
3 - n = -1 => n = 4
3 - n = -2 => n = 5
3 - n = -4 => n = 7
Vậy : n \(\in\){ 2 ; 1 ; -1 ; 4 ; 5 ; 7 }
Ta có \(M=\frac{\frac{3}{5}+\frac{3}{7}-\frac{3}{11}}{\frac{4}{5}+\frac{4}{7}-\frac{4}{11}}=\frac{3\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{4\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}=\frac{3}{4}\)
32 x 48 + 48 : 6 - 123 : 3
= 1536 + 8 - 41
= 1544 - 41
= 1503
\(\left(\frac{1}{3}+\frac{3}{4}-\frac{13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=\left(\frac{4}{12}+\frac{9}{12}-\frac{13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=\left(\frac{4+9-13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=0:\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=0\)
Study well ! >_<
(13 +34 - 1312 ) : (1213 + 123234 +12342345 )
=\(\left(\frac{4}{12}+\frac{9}{12}-\frac{13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
= \(\left(\frac{4+9-13}{12}\right):\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
= \(0:\left(\frac{12}{13}+\frac{123}{234}+\frac{1234}{2345}\right)\)
\(=0\)
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Dành riêng luôn
\(-\frac{1123}{123}+123-\frac{1234}{3456}\)
\(=\frac{14006}{123}-\frac{1234}{3456}\)
\(=113,5128585\)