a) Ta có : 

990 = 2.3².5.11

2610=2.3².5.29

ƯCLN(990;2610) = 2.3².5=90

\(\Rightarrow\frac{990}{2610}=\frac{990:90}{2610:90}=\frac{11}{29}\)

Tương tự với câu b) 

\(a,\frac{990}{2610}=\frac{990:90}{2610:90}=\frac{11}{29}\)

\(b,\frac{374}{506}=\frac{374:2}{506:2}=\frac{187}{253}=\frac{187:11}{253:11}=\frac{17}{23}\)

\(c,\frac{3600-75}{8400-175}=\frac{3525}{8225}=\frac{3525:25}{8225:25}=\frac{141}{329}\)

\(d,\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{9^{12}.9^2.25^3.25^2.8^3.8^4}{\left(9.2\right)^{12}.\left(25.25\right)^3.\left(8.3\right)^3}=\frac{9^{12}.9^2.25^3.25^2.8^3.8^3.8}{9^{12}.2^{12}.25^3.25^2.25.8^3.3^3}=\frac{9^2.8}{2^{12}.25.3^3}\) đến đây bn tự làm nốt đi! 

~ mỏi ~

lấy bài của chị đúng ko em

\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)

\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{25}.5^{12}}\)

\(=\frac{3^3.1.1}{1.1.5^2}\)

\(=\frac{27}{25}\)

Ta có: \(\dfrac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)= \(\dfrac{9^{14}.25^5.8^7}{9^{12}.2^{12}.\left(25^2\right)^3.8^3.3^3}\)=\(\dfrac{9^{12}.9^2.25^5.8^7}{9^{12}.2^{12}.25^6.8^3.3^3}\)

= \(\dfrac{9^{12}.3^4.25^5.8^7}{9^{12}.\left(2^{12}.8^3\right).25^5.25.3^3}\)=\(\dfrac{9^{12}.3^3.3.25^5.8^7}{9^{12}.8^7.25^5.25.3^3}\)=\(\dfrac{\left(9^{12}.3^3.25^5.8^7\right).3}{\left(9^{12}.3^3.25^5.8^7\right).25}\)

=\(\dfrac{3}{25}\)

( Có một vài bước mik làm tắt bặn nhé!)

a) 2012 - ( 304 + 2012 ) + ( 2013 + 304 )

= 2012 - 304 - 2012 + 2013 + 304 

= 2012 + ( - 304 ) + ( - 2012 ) + 2013 + 304

= [ 2012 + ( - 2012 ) ] + [ ( - 304 ) + 304 ] + 2013

= 0 + 0 + 2013

= 2013

b) \(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)

\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(3^2.2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{3^{24}.2^{12}.5^{12}.2^9.3^3}\)

\(=\frac{3^{28}.5^{10}.2^{21}}{3^{27}.5^{12}.2^{21}}\)

\(=\frac{3}{5^2}=\frac{3}{25}\)

a) 2012 - ( 304 + 2012 ) + (2013 + 304 )

= 2012 - 304 +2012 + 2013 + 304

= ( 2012 - 2012 ) + ( 304 + 304 ) + 2013

= 0 + 608 + 2013

= 2621

Chờ một chút để minh suy nghĩ 

ok bạn

a, \(\dfrac{990}{2610}=\dfrac{11}{29}\)

b) \(\dfrac{3600-75}{8400-175}=\dfrac{3}{7}\)

c) \(\dfrac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^5\cdot24^3}=\dfrac{3}{25}\)

\(\frac{-72}{14}=\frac{-36}{7}\)

\(\frac{990}{2610}=\frac{11}{29}\)

\(\frac{374}{506}=\frac{17}{23}\)

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

hok tốt!!

\(\frac{990}{2610}=\frac{990:11}{2610:11}=\frac{11}{29}\)

\(\frac{374}{506}=\frac{374:22}{506:22}=\frac{17}{23}\)

\(\frac{3600-75}{8400-175}=\frac{3525}{8225}=\frac{3525:1175}{8225:1175}=\frac{3}{7}\)

\(\frac{9^{14}.255^5.8^7}{18^{12}.625^3.24^3}=\frac{3^{28}.5^5.3^5.17^5.2^{21}}{2^{12}.3^{24}.5^{12}.2^9.3^3}=\frac{3^{33}.5^5.17^5.2^{21}}{2^{21}.3^{27}.5^{12}}=\frac{3^6.17^5}{5^7}\)