1:a)\(\frac{28^{15}\cdot3^{17}}{84^{16}}\)=\(\frac{28^{15}\cdot3^{15}\cdot3^2}{84^{16}}\)=\(\frac{\left(28^{15}\cdot3^{15}\right)\cdot3^2}{84^{16}}\)=\(\frac{84^{15}\cdot9}{84^{16}}\)=\(\frac{9}{84}\)=\(\frac{3}{28}\)

b)\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)=\(\frac{3^2\cdot3^8+2^2\cdot3^2}{5\cdot3^8+5\cdot4}\)=\(\frac{9\cdot3^8+4\cdot9}{5\cdot\left(3^8+4\right)}\)=\(\frac{9\cdot\left(3^8+4\right)}{5\cdot\left(3^8+4\right)}\)=\(\frac{9}{5}\)

Xét vế trái ta có:72^15=3^15*24^15=3^15*24^9*24^6

=3^15*24^9*12^6*2^6=3^15*24^9*12^6*4^3(1)

Xét vế phải ta có: 3^21*96^9=3^15*3^6*24^9*4^9

=3^15*3^6*24^9*4^6*4^3=3^15*24^9*(3^6*4^6*4^3)

=3^15*24^9*(12^6*4^3)(2)

từ (1) và (2)=>72^15=3^21*96^9

1) \(\frac{3^{10}+6^2}{5\cdot3^8+20}=\frac{3^{10}+3^2\cdot2^2}{5\cdot3^8+5\cdot2^2}=\frac{3^2\left(3^8+2^2\right)}{5\left(3^8+2^2\right)}=\frac{9}{5}\)

2) \(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{28^{15}\cdot3^{17}}{28^{16}\cdot3^{16}}=\frac{3}{28}\)

mình cần cách làm nha các bạn , giúp mình với !
 

\(\frac{3^{10}+6^2}{5.3^8+20}\)\(=\frac{3^2+2^2.3^2}{5+2^2.5}=\frac{3^2\left(1+2^2\right)}{5\left(1+2^2\right)}\)\(=\frac{3^2}{5}\)\(=\frac{9}{5}\)

Phân tích ra : VD : 4¹⁵=(2²)¹⁵=2^2.15=2³⁰

Nếu làm thế này thì sẽ dể hơn vì sẽ có nhiều  lũy thừa giống nhau và dễ chiệt tiêu hơn nhé bạn >

\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)   

\(=\frac{3^{10}+\left(3\cdot2\right)^2}{5\left(3^8+4\right)}\)   

\(=\frac{3^{10}+3^2\cdot2^2}{5\left(3^8+4\right)}\)   

\(=\frac{3^2\left(3^8+4\right)}{5\left(3^8+4\right)}\)   

\(=\frac{9}{5}\)

\(a.\frac{3}{28}\)

\(b.\frac{9}{5}\)

Bây giờ mình sẽ viết đầy đủ hơn nhé:

a) \(\frac{28^{15}.3^{17}}{84^{16}}=\frac{\left(28.3\right)^{15}.3^2}{\left(28.3\right)^{15}.84}=\frac{9}{84}=\frac{3}{28}\)

b)\(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^{10}+2^2.3^2}{5.3^8+20}=\frac{3^2.\left(3^8+2^2\right)}{5.\left(3^8+2^2\right)}\)\(=\frac{9}{5}\)

có 

a) \(\frac{28^{15}.3^{17}}{84^{16}}=\frac{\left(2^2.7\right)^{15}.3^{17}}{\left(2^2.3.7\right)^{16}}=\frac{2^{30}.7^{15}.3^{17}}{2^{32}.3^{16}.7^{16}}=\frac{3}{2^2.7}=\frac{3}{28}\)

b) \(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^{10}+\left(2.3\right)^2}{5.3^9+2^2.5}=\frac{3^{10}+2^2.3^2}{5\left(3^8.2^2\right)}=\frac{3^2.\left(3^8+2^2\right)}{5.\left(3^8+2^2\right)}=\frac{3^2}{5}=\frac{9}{5}\)

\(\frac{7.4^5.3^{11}+2^{13}.9^5}{6^{10}+2^{12}.3^{10}}=\frac{7.\left(2^2\right)^5.3^{11}+2^{13}.\left(3^2\right)^5}{\left(2.3\right)^{10}+2^{12}.3^{10}}=\frac{7.2^{10}.3^{11}+2^{13}.3^{10}}{2^{10}.3^{10}+2^{12}.3^{10}}\)

\(=\frac{2^{10}.3^{10}.\left(7.3+2^3\right)}{2^{10}.3^{10}.\left(1+2^2\right)}=\frac{7.3+2^3}{1+2^2}=\frac{29}{5}\)