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

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

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

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

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

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 !
 

So sánh: 72¹⁵ và 3²¹.96⁹

72¹⁵=(2³.3²)¹⁵=(2³)¹⁵.(3²)¹⁵=2⁴⁵.3³⁰

3²¹.96⁹=3²¹.(3.2⁵)⁹=3²¹.3⁹.(2⁵)⁹=3²¹⁺⁹.2⁴⁵=3³⁰.2⁴⁵

Vì 2⁴⁵.3³⁰ = 30³⁰.2⁴⁵

Nên 72¹⁵ = 3²¹.96⁹

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

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

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

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

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

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

\(P=\dfrac{4\cdot36^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)

\(=\dfrac{4\cdot\left(2^2\cdot3^2\right)^4-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^8\cdot3^8\cdot2^2\cdot5}\)

\(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\)

\(=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{-2}{6}=-\dfrac{1}{3}\)

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