Question

1) Rút gọn biểu thức

A=\(\frac{3600-75}{8400-175}\)

B=\(\frac{9^{14}.25^7.8^7}{18^{12}.625^3.24^3}\)

C=\(\frac{1+3+5+...+19}{21+23+25+...+39}\)

D=\(\frac{71.52+53}{530.71-180}\)

Answer 1

\(A=\frac{3600-75}{8400-175}=\frac{3525}{8225}=\frac{3}{7}\)

\(B=\frac{9^{14}.25^7.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(5^2\right)^7.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}=\frac{3^{28}.5^{14}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3^3}=\frac{3^{28}.5^{14}.2^{21}}{2^{21}.3^{27}.5^{12}}=3.5^2=3.25=75\)

\(C=\frac{1+3+5+...+19}{21+23+25+...+39}=\frac{\left(19+1\right).10:2}{\left(39+21\right).10:2}=\frac{100}{300}=\frac{1}{3}\)

\(D=\frac{71.52+53}{530.71-180}=\frac{3745}{37450}=\frac{1}{10}\).