Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
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) \(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^{10}+\left(2.3\right)^2}{5.3^9+2^2.5}=\frac{3^{10}+2^2.3^2}{5\left(3^8.2^2\right)}=\frac{3^2.\left(3^8+2^2\right)}{5.\left(3^8+2^2\right)}=\frac{3^2}{5}=\frac{9}{5}\)
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
\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)
\(=\frac{3^{10}+\left(3\cdot2\right)^2}{5\left(3^8+4\right)}\)
\(=\frac{3^{10}+3^2\cdot2^2}{5\left(3^8+4\right)}\)
\(=\frac{3^2\left(3^8+4\right)}{5\left(3^8+4\right)}\)
\(=\frac{9}{5}\)
Bài 1 : Bài giải
\(\frac{28^{15}\cdot3^{17}}{84^{16}}=\frac{\left(2^2\cdot7\right)^{15}\cdot3^{17}}{\left(2^2\cdot3\cdot7\right)^{16}}=\frac{2^{30}\cdot7^{15}\cdot3^{17}}{2^{32}\cdot3^{16}\cdot7^{16}}=\frac{3}{2^2\cdot7}=\frac{3}{4\cdot7}=\frac{3}{28}\)
Bài 2 : Bài giải
\(\frac{3^6\cdot21^{12}}{175^9\cdot7^3}=\frac{3^6\cdot\left(3\cdot7\right)^{12}}{\left(5^2\cdot7\right)^9\cdot7^3}=\frac{3^6\cdot3^{12}\cdot7^{12}}{5^{18}\cdot7^9\cdot7^3}=\frac{3^{18}\cdot7^{12}}{5^{18}\cdot7^{12}}=\frac{3^{18}}{5^{18}}\)
\(\frac{3^{10}\cdot6^7\cdot4}{10^9\cdot5^8}=\frac{3^{10}\cdot\left(2\cdot3\right)^7\cdot2^2}{\left(2\cdot5\right)^9\cdot5^8}=\frac{3^{10}\cdot2^7\cdot3^7\cdot2^2}{2^9\cdot5^9\cdot5^8}=\frac{3^{17}\cdot2^9}{2^9\cdot5^{17}}=\frac{3^{17}}{5^{17}}\)
Ta có : \(3^{17}\cdot5^{18}=3^{17}\cdot5^{17}\cdot5=\left(3\cdot5\right)^{17}\cdot5=15^{17}\cdot5\)
\(3^{18}\cdot5^{17}=3\cdot3^{17}\cdot5^{17}=3\cdot\left(3\cdot5\right)^{17}=3\cdot15^{17}\)
\(\text{ Vì }5\cdot15^{17}>3\cdot15^{17}\text{ }\Rightarrow\text{ }3^{17}\cdot5^{18}>3^{18}\cdot5^{17}\text{ }\Rightarrow\text{ }\frac{3^{18}}{5^{18}}< \frac{3^{17}}{5^{17}}\)
\(\frac{3^{10}+6^2}{5.3^8+20}\)
\(=\frac{3^2+2^2.3^2}{5+2^2.5}=\frac{3^2\left(1+2^2\right)}{5\left(1+2^2\right)}\)\(=\frac{3^2}{5}\)\(=\frac{9}{5}\)
Rut gon bieu thuc ( 2x like )
a)28^15 . 3^17
_____________
84^16
b) 3^10 + 6^2
________________
5.3^8 + 20
28^15x3^17/84^16
=28^15x3^17/(28x3)^16
=28^15x3^17/28^16x28^16
=3/28
