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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
\(\frac{3^{10}+6^2}{5.3^8+20}\)\(=\frac{3^2+2^2.3^2}{5+2^2.5}=\frac{3^2\left(1+2^2\right)}{5\left(1+2^2\right)}\)\(=\frac{3^2}{5}\)\(=\frac{9}{5}\)
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 : \(3^{17}\cdot5^{18}=3^{17}\cdot5^{17}\cdot5=\left(3\cdot5\right)^{17}\cdot5=15^{17}\cdot5\)
\(3^{18}\cdot5^{17}=3\cdot3^{17}\cdot5^{17}=3\cdot\left(3\cdot5\right)^{17}=3\cdot15^{17}\)
\(\text{ Vì }5\cdot15^{17}>3\cdot15^{17}\text{ }\Rightarrow\text{ }3^{17}\cdot5^{18}>3^{18}\cdot5^{17}\text{ }\Rightarrow\text{ }\frac{3^{18}}{5^{18}}< \frac{3^{17}}{5^{17}}\)
Ta có : 7215 = (23.32)15 = 245.330
321.969 = 321.(25.39) = 330.245
Suy ra 7215 = 321.969
Ta có: 7515 = ( 23 . 33 )15 = 245 . 330
3121 . 969 = 321 . ( 25 . 39 ) = 330 . 245
\(\Rightarrow\) 7515 = 3121 . 969
Chúc bạn hok tốt!!!Nguyễn Hoàng Linh
\(A=\frac{2^{10}.3^8-2.2^9.3^9}{2^{10}.3^8+2^8.3^8.2^2.5}\)
\(A=\frac{2^{10}.3^8-2^{10}.3^9}{2^{10}.3^8+2^{10}.3^8.5}\)
\(A=\frac{2^{10}.3^8\left(1-3\right)}{2^{10}.3^8\left(1+5\right)}\)
\(A=\frac{1-3}{1+5}\)
\(A=-\frac{1}{3}\)
Bài làm
\(C=-\frac{3}{5}.\frac{20}{135}.\frac{-7}{1400}.\frac{250}{3}.\frac{27}{10}\)
\(C=\frac{-3}{5}.\frac{4}{27}.\frac{-1}{200}.\frac{250}{3}.\frac{27}{10}\)
\(C=\frac{-3.4.\left(-1\right).250.27}{5.27.200.3.10}\)
\(C=\frac{1}{10}\)
Vậy \(C=\frac{1}{10}\)
# Học tốt #
C = \(\frac{-3}{5}\cdot\frac{20}{135}\cdot\frac{-7}{1400}\cdot\frac{250}{3}\cdot\frac{27}{10}\) C = \(\left(\frac{-3}{5}\cdot\frac{250}{3}\right)\cdot\left(\frac{20}{135}\cdot\frac{27}{10}\right)\cdot\frac{-7}{1400}\) C = \(-50\cdot\frac{2}{5}\cdot\frac{-7}{1400}\) C = \(-20\cdot\frac{-7}{1400}\) C = \(\frac{1}{10}\)
1
a) \(\frac{2^2.9^2}{6^4.8}\)\(=\frac{2^2+\left(3^2\right)^2}{\left(2.3\right)^4.2^3}\)\(=\frac{3^4}{2^4.3^4.2}=\frac{1}{2^4.2}=\frac{1}{2^5}=\frac{1}{32}\)
b)\(\frac{3^{10}.2^1}{16.4^3.243}=\frac{3^{10}.2^1}{2^4.4^3.3^5}=\frac{3^5}{2^3.4^3}=\frac{3^5}{\left(2.4\right)^3}\)\(=\frac{3^5}{8^3}=\frac{243}{512}\)
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