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\(a)10^{19}+10^{18}+10^{17}\\ =10^{17}\cdot\left(10^2+10+1\right)\\ =10^{17}\cdot111=10^{16}\cdot2\cdot5\cdot111\\ =10^{16}\cdot2\cdot555\\ \Rightarrow10^6\cdot2\cdot555⋮555\\ hay:10^{19}+10^{^{ }18}+10^{17}⋮555\)
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a) \(\frac{x-3}{5}=\frac{4}{9}\)
=> ( x - 3) . 9 = 20
=> 9x - 27 = 20
=> 9x = 47
=> x = \(\frac{47}{9}\)
b) \(\left(x-\frac{1}{4}\right)^2:3^2=81\)
\(\Rightarrow\left(x-\frac{1}{3}\right)^2:9=81\)
\(\Rightarrow\left(x-\frac{1}{4}\right)^2=729\)
\(\Rightarrow x-\frac{1}{4}=27\) hoặc \(x-\frac{1}{4}=-27\)
+) \(x-\frac{1}{4}=27\Rightarrow x=\frac{109}{4}\)
+) \(x-\frac{1}{4}=-27\Rightarrow x=\frac{-107}{4}\)
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Ta có : \(\left\{{}\begin{matrix}2^{24}=\left(2^3\right)^8=8^8\\3^{16}=\left(3^2\right)^8=9^8\end{matrix}\right.\)
Thấy : \(9>8\)
\(\Leftrightarrow9^8>8^8\)
\(\Leftrightarrow3^{16}>2^{24}\)
Vậy ...
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\(3^{2x+4}:3^{x+1}=81\)
\(3^{2x+4-x-1}=3^4\)
\(3^{x+3}=3^4\)
\(\Rightarrow x+3=4\)
\(\Rightarrow x=1\)
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C = \(\left(\frac{1}{2^2}-1\right)\left(\frac{1}{3^2}-1\right).......\left(\frac{1}{9^2}-1\right)\left(\frac{1}{10^2}-1\right)\)
= \(\frac{-3}{2^2}.\frac{-8}{3^2}.............\frac{-80}{9^2}.\frac{-99}{10^2}\)
= \(-\left(\frac{1.3}{2^2}.\frac{2.4}{3^2}..........\frac{8.10}{9^2}.\frac{9.11}{10^2}\right)\)
= \(-\frac{\left(1.2.3......8.9\right)\left(3.4.5........10.11\right)}{\left(2.3.4......9.10\right)\left(2.3.4......9.10\right)}=-\frac{1.11}{10.2}=-\frac{11}{20}\)
\(\sqrt{\frac{1}{10}-\sqrt{\frac{4}{9}}=-0.3}\):
\(-0.3:\sqrt{\frac{81}{16}=-0.1}\)
VẬY KẾT QUẢ BẰNG -0.1
\(\left(\sqrt{\frac{1}{10}}-\sqrt{\frac{4}{9}}\right):\sqrt{\frac{81}{16}}\)
\(=-0,3504389006:\sqrt{\frac{81}{16}}\)
Em ơi,bài này ra dư lắm