\(\frac{5^2.25^4}{125^3}=\frac{5^2.\left(5^2\right)^4}{\left(5^3\right)^3}=\frac{5^2.5^8}{5^9}=\frac{5^{10}}{5^9}=5.\)

a) \(3^2.\frac{1}{243}.81^2.\frac{1}{3^2}=\frac{1.81^2}{243}.\frac{3^2}{3^2}=\frac{6561}{243}.1=27\)

b, \(4^6.256^2.2^4=2^{12}.2^{16}.2^4=2^{32}\)

c)  \(A=\frac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}\)(Mình rút gọn lun cho nhanh nhé ) \(\Rightarrow A=\frac{4}{5}\)

d) \(\Rightarrow B=70\)k cho mình nha Cô Nàng Họ Dương

Đây nhé : ý a,b mình đã giải thích rồi 

c) \(=\frac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2.6}{3.5}=\frac{12}{15}=\frac{4}{5}\)\(\frac{4}{5}\)

d) \(=\frac{2^4.5^4+2^5.5^3}{2^3.5^2}=\frac{2^4.5^3.\left(5+2\right)}{2^3.5^2}=2.5.7=70\)

Ta có : 3^x + 3^{x + 2} = 810

=> 3^x(1 + 3²) = 810

=> 3^x.10 = 810

=> 3^x = 81

=> 3^x = 3⁴

=> x = 4

ta có \(3^3+3^x+2=810\)

=>\(3^x\left(1+3^2\right)=810\)

=>\(3^x.10=810\)

=>\(3^x=81\)

=>\(3^x=3^4\)

=>x=4

Vậy x=4

\(\frac{3}{5}-\frac{3}{25}-\frac{3}{125}\)

\(=\frac{75}{125}-\frac{15}{125}-\frac{3}{125}\)

\(=\frac{57}{125}\)

_______________________________

\(\frac{7}{5}-\frac{7}{25}-\frac{7}{125}\)

\(=\frac{175}{125}-\frac{35}{125}-\frac{7}{125}\)

\(=\frac{133}{125}\)

eo ơi đưa về lũy thừa của các số nguyên tố là xong      

\(\frac{27^2.15^3.125^{17}.10^{10}.3^8.512+1024.25^{28}.12^6.15^7}{125.6^{17}+625^{12}.6^{13}.125^2.25^5.16}\)

=\(\frac{3^6.3^3.5^3.5^{34}.2^{10}.5^{10}.3^8.2^9+2^{10}.5^{56}.3^6.2^{12}.3^7.5^7}{5^{63}.6^{17}+5^{48}.6^{13}.5^6.2^4}\)=\(\frac{3^{17}.5^{47}.2^{19}+2^{22}.5^{63}.3^{13}}{5^{63}.6^{17}+5^{48}.6^{13}.5^6.2^4}=\frac{3^{13}.5^{47}.2^{19}.3^4+2^{19}.5^{47}.3^{13}.2^3.5^{16}}{5^{54}.6^{13}.5^9+5^{54}.6^{13}.2^4}\)

=\(\frac{3^{13}.5^{47}.2^{19}\left(3^4+2^3.5^{16}\right)}{5^{54}.6^{13}\left(5^9+2^4\right)}=\frac{6^{13}.2^6.5^{47}\left(3^4+2^3.5^{16}\right)}{5^7.5^{47}.6^{13}\left(5^9+2^4\right)}=\frac{2^6\left(3^4+2^3.5^{16}\right)}{5^7\left(5^9+2^4\right)}\)

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