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\(\frac{4^{11}.15+4^{10}.85}{16^3.20}=\frac{4^{10}.\left(4.15+85\right)}{\left(4^2\right)^3.4.5}=\frac{4^{10}.145}{4^7.5}=4^3.29\)
a, 89 - (73 - \(x\)) = 20
73 - \(x\) = 89 - 20
73 - \(x\) = 69
\(x\) = 73 - 69
\(x\) = 4
b, 7\(x\) - 2\(x\) = 617:615 + 44:11
5\(x\) = 62 + 4
5\(x\) = 36 + 4
5\(x\) = 40
\(x\) = 40: 5
\(x\) = 8
( 4 . 315 + 5 . 315 ) : 316
= 315.( 4 + 5) : 316
= 315.32:316
= 31=3
\(=\left[3^{15}\left(4+5\right)\right]:3^{16}=\left(3^{15}.3^2\right):3^{16}=3^{17}:3^{16}=3\)
\(A,\frac{4^9.36+64}{16^4.100}=\frac{\left(2^2\right)^9.2^2.3^2+2^6}{\left(2^4\right)^4.2^2.5^2}=\frac{2^{20}.3^2+2^6}{2^{18}.5^2}=\frac{2^6\left(2^{14}.3^2+1\right)}{2^{18}.5^2}=\frac{2^{14}.3^2+1}{2^{12}.5^2}=\frac{147457}{102400}\)
B,
\(\frac{11.3^{22}.3-9^{13}}{\left(2.3^{14}\right)^2}=\frac{11.3^{22}-\left(3^2\right)^{13}}{2^2.3^{28}}=\frac{11.3^{22}-3^{26}}{2^2.3^{28}}=\frac{3^{22}\left(11.1-3^4\right)}{2^2.3^{28}}=\frac{11-81}{2^2.3^6}=-\frac{70}{2916}=-\frac{35}{1456}\)
c,
\(\frac{45^3.20^4.18}{180^5}=\frac{\left(3^2.5\right)^3.\left(5.2^2\right)^4.2.3^2}{\left(2^2.3^2.5\right)^5}=\frac{3^6.5^3.5^4.2^8.2.3^2}{2^{10}.3^{10}.5^5}=\frac{3^8.2^{10}.5^7}{2^{10}.3^{10}.5^5}=\frac{5^2}{3^2}=\frac{25}{9}\)
\(\frac{4^9\cdot36+64}{16^4\cdot100}=\frac{2^6\cdot147457}{2^{16}\cdot100}=\frac{147457}{2^{10}\cdot100}\)
\(\frac{11\cdot3^{22}\cdot3-9^{13}}{2^2\cdot3^{28}}=\frac{3^{23}\left(11-3^3\right)}{2^2\cdot3^{28}}=\frac{-16\cdot3^{23}}{2^2\cdot3^{28}}=\frac{-4}{243}\)
\(\frac{45^3\cdot20^4\cdot18}{180^5}=\frac{3^8\cdot2^9\cdot5^7}{2^{10}\cdot3^{10}\cdot5^5}=\frac{25}{18}\)
\(a;5^{23}=5\cdot5^{22}< 6\cdot5^{22}\Rightarrow5^{23}< 6\cdot5^{22}\)
\(b;7\cdot2^{13}< 8\cdot2^{13}=2^3\cdot2^{13}=2^{15}\)
\(c;21^{15}=3^{15}\cdot7^{15}>3^{15}\cdot7^{14}=27^5\cdot49^8\)
\(d;199^{20}< 200^{20}=10^{40}\cdot2^{20}< 10^{45}\cdot2^{15}=2000^{15}< 2001^{15}\)
\(e;3^{39}=9^{13}< 11^{13}< 11^{21}\)
\(\left(x+3\right)^{20}=\left(x+3\right)^{15}\)
\(\Leftrightarrow\left(x+3\right)^5\cdot\left(x+3\right)^{15}=\left(x+3\right)^{15}\)
\(\Leftrightarrow\left(x+3\right)^5=1\)
\(\Leftrightarrow x+3=1\)
\(\Leftrightarrow x=-2\)
(x+3)20=(x+3)15
(x+3)20-(x+3)15=0
(x+3)15 . [(x+3)5-1]=0
* (x+3)15=0 * (x+3)5-1=0
x+3=0 (x+3)5=1
x=0-3 x+3=1
x=-3 x=1-3
x=-2
Vậy x=-3 hoặc x=-2
a) \(\frac{4^2.25^2+32,125}{2^3.5^2}=\frac{\left(4.25\right)^2+32,125}{8.25}=\frac{100^2+32,125}{200}=\frac{10000+32,125}{200}=\frac{10032,125}{200}=50,160625\)
b) \(\frac{4^5.9^4.2.6^9}{2^{10}.3^8+20}=\frac{2^{10}.3^8.2.2^9.3^9}{2^{10}.3^8+2^2.5}=\frac{2^{10}.3^9}{2^2.5}=\frac{20155392}{20}=1007769,6\)
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