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a, \(\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}=\frac{2^{13}.\left(2^{17}.5^7+5^{27}\right)}{2^{10}.\left(2^{17}.5^7+5^{27}\right)}=\frac{2^{13}}{2^{10}}=2^3=8\).
b, \(\frac{81.2^2+3^4+20.9^2}{16.3^2+45+2^2.9}=\frac{3^4.2^2+3^4+20.3^4}{16.3^2+3^2.5+2^2.3^2}=\frac{3^4.\left(2^2+1+20\right)}{3^2.\left(16+5+2^2\right)}=\frac{3^4.25}{3^2.25}=\frac{3^4}{3^2}=3^2=9\)
a: \(=\dfrac{2^{13}\cdot5^7\left(2^{17}+5^{20}\right)}{2^{10}\cdot5^7\left(2^{17}+5^{20}\right)}=2^3\)
b: \(M=\left(7-4\right)^{\left(7-5\right)^{\left(7-6\right)^{\left(7+6\right)^{\left(7+5\right)}}}}\)
\(=3^{2\cdot1\cdot13\cdot12}=3^{312}\)
\(\Leftrightarrow2^x=\dfrac{2^{30}\cdot5^7+2^{13}\cdot5^{27}}{2^{27}\cdot5^7+2^{10}\cdot5^{27}}\)
\(\Leftrightarrow2^x=\dfrac{2^{13}\cdot5^7\left(2^{17}+5^{20}\right)}{2^{10}\cdot5^7\left(2^{17}+5^{20}\right)}=2^3\)
=>x=3
\(A=\frac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}\)
\(=\frac{2^3\left(2^{27}.5^7+2^{10}.5^{27}\right)}{2^{27}.5^7+2^{10}.5^{27}}\)
\(=2^3=8\)
Dấu " / " là phân số nhé :
a) 5 5/27 + 7/23 + 0,5 - 5/27 + 16/23
= 140/27 + 7/23 + 1/2 - 5/27 + 16/23
= ( 140/27 - 5/27 ) + ( 7/23 + 16/23 ) + 1/2
= 5 + 1 + 1/2
= 6 + 1/2
= 13/2
b) 3/8 . 27 1/5 - 51 .1/5 . 3/8 + 19
= 3/8 . 136/5 - 51 . 1/5 . 3/8 + 19
= 3/8 . ( 136/5 - 1/5 ) - 51 + 19
= 3/8 . 27 - 51 + 19
= 81/8 - 52 + 19
= -183/8
Sorry nha mik sửa lại con B
b) 3/8 . 27 1/5 - 51 . 1/5 . 3/8 + 19
= 3/8 . 136/5 - 51/5 . 3/8 + 19
= 3/8 . ( 136/5 - 51/5 ) + 19
= 3/8 . 17 + 19
= 51/8 + 19
= 203/8
\(\frac{\left(\frac{53}{4}-\frac{59}{27}-\frac{65}{6}\right).\frac{5751}{25}+\frac{187}{4}}{\left(\frac{10}{7}+\frac{10}{3}\right):\left(\frac{37}{3}-\frac{100}{7}\right)}=\frac{\left(\frac{4293}{324}-\frac{708}{324}-\frac{3510}{324}\right).\frac{5751}{25}+\frac{187}{4}}{\left(\frac{30}{21}+\frac{70}{21}\right):\left(\frac{259}{21}-\frac{300}{21}\right)}=\frac{\frac{25}{108}.\frac{5751}{25}+\frac{187}{4}}{\frac{100}{21}:\left(-\frac{41}{21}\right)}\)=\(\frac{\frac{213}{4}+\frac{187}{4}}{-\frac{100}{41}}=100:\left(-\frac{100}{4}\right)=-4\)
\(30+\frac{14}{5}:\left(\frac{24}{150}-\frac{270}{150}-\frac{25}{150}\right)=30+\frac{14}{5}:\left(-\frac{271}{150}\right)=30+\left(-\frac{420}{271}\right)=\frac{7710}{271}\)
\(\dfrac{2^{30}.5^7+2^{13}.5^{27}}{2^{27}.5^7+2^{10}.5^{27}}=\dfrac{2^{13}.5^7.\left(2^{17}+5^{20}\right)}{2^{10}.5^7.\left(2^{17}+5^{20}\right)}= \dfrac{2^{13}.5^7}{2^{10}.5^7}=2^3=8\)