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\(\dfrac{75.5^4+175.5^4}{20.25.125-625.75}\)
\(=\dfrac{5^4\left(175+75\right)}{4.5.5^2.5^3-5^4.5^2.3}=\dfrac{5^4.225}{4.5^6-3.5^6}\)
\(=\dfrac{5^4.225}{4.5^6-3.5^6}=\dfrac{5^4.15^2}{5^6\left(4-3\right)}=\dfrac{5^4.\left(5.3\right)^2}{5^6}=\dfrac{5^4.5^2.3^2}{5^6}=\dfrac{5^6.3^2}{5^6}=9\)
Bài làm
\(A=\frac{2^2.10+2^3.6}{2^2.15-2^4}\)
\(A=\frac{2^2.10+2.2^2.6}{2^2.15-2^2.2^2.1}\)
\(A=\frac{2^2.\left(10+6\right).2}{2^2.\left(15-1\right).2^2}\)
\(A=\frac{2^2.16.2}{2^2.14.2^2}\)
\(A=\frac{16}{14.2}\)
\(A=\frac{8}{7.2}\)
\(A=\frac{8}{14}\)
\(A=\frac{4}{7}\)
Vậy \(A=\frac{4}{7}\)
\(B=\frac{2^9.15^{17}.75^3}{18^8.5^{24}.9^2}\)
\(B=\frac{2^9.\left(3.5\right)^{17}.\left(3.5^2\right)^3}{\left(2.3^2\right)^8.5^{24}.\left(3^2\right)^2}\)
\(B=\frac{2^9.3^{17}.5^{17}.3^3.5^6}{2.3^{19}.5^{24}.3^4}\)
\(B=\frac{2^8.1.1.1.5}{1.3^2.1.3}\)
\(B=\frac{2^8.5}{3^3}\)
\(B=\frac{1280}{27}\)
75.54+175.54
20.25.125-625.75
=(75+175).54
20.5.5.125-625.75
=250.54
100.625-625.75
=250.54
625.(100-75)
=250.54
54.25
=250
25
=10