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a) \(\left[\left(-2,7\right)^4\right]^5-\left[\left(-2,7\right)^2\right]^{20}\)
\(=\left(-2,7\right)^{20}-\left(-2,7\right)^{20}\)
\(=0\)
b) \(\left(-0,5\right)^5:\left(-0,5\right)^3-\left(\dfrac{17}{2}\right)^7:\left(\dfrac{17}{2}\right)^6\)
\(=\left(-0,5\right)^2-\dfrac{17}{2}\)
\(=0,25-\dfrac{17}{2}\)
\(=-8,25\)
c) \(\left(8^{14}:4^{12}\right):\left(16^6:8^2\right)\)
\(=8^{14}:4^{12}:16^6\cdot8^2\)
\(=2^{48}:2^{24}:2^{24}\)
\(=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(\frac{A}{2}=\frac{3^3}{2}-\frac{5^3}{6}+\frac{7^3}{12}-\frac{9^3}{20}+\frac{11^3}{30}-\frac{13^3}{42}+\frac{15^3}{56}-\frac{17^3}{72}+...+\frac{199^3}{9900}\)
\(=3^2.\left(1+\frac{1}{2}\right)-5^2.\left(\frac{1}{2}+\frac{1}{3}\right)+7^2.\left(\frac{1}{3}+\frac{1}{4}\right)-9^2.\left(\frac{1}{4}+\frac{1}{5}\right)+...+199^2.\left(\frac{1}{99}+\frac{1}{100}\right)\)
\(=3^2+\left(\frac{3^2}{2}-\frac{5^2}{2}\right)-\left(\frac{5^2}{3}-\frac{7^2}{3}\right)+\left(\frac{7^2}{4}-\frac{9^2}{4}\right)-\left(\frac{9^2}{5}-\frac{11^2}{5}\right)+...+\left(\frac{197^2}{99}-\frac{199^2}{99}\right)+\frac{199^2}{100}\)
\(=3^2-8+8-8+...+8+\frac{199^2}{100}=3^2+\frac{199^2}{100}< 3^2+\frac{199.200}{100}=9+398=407\)
\(\Rightarrow A< 407.2=814\)
![](https://rs.olm.vn/images/avt/0.png?1311)
A)-2410/999
b)10771/3330
c)529/990
Nhớ ấn đúng để cộng điểm cho mình nha
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(8^{14}:4^{12}\right):\left(16^0:8^2\right)\)
\(=\left(2^{42}:2^{24}\right):\left(1:2^6\right)\)
\(=2^{18}:\frac{1}{2^6}=2^{18}.2^6\)
\(=2^{24}\)
(814 : 412) : (160 : 82)
= (242 : 224 ) : ( 1 : 26 )
= 218 . 26
= 224