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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) \(\left(8^{14}:4^{12}\right):\left(16^6:8^2\right)\)
\(=8^{14}:4^{12}:16^6\cdot8^2\)
\(=2^{48}:2^{24}:2^{24}\)
\(=0\)
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\(A=x^3+x^2y-2x^2-xy-y^2+3y+x+2019\)
\(=x^3+x^2\left(2-x\right)-2x^2-y\left(x+y\right)+3y+x+2019\)
\(=x^3+2x^2-x^3-2x^2-2y+3y+x+2019\)
\(=x+y+2019=2021\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(M=\frac{8^{20}+4^{20}}{4^{25}+64^5}\)
\(=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)
\(=\frac{2^{60}+2^{40}}{2^{50}+2^{30}}\)
\(=\frac{2^{40}\left(2^{20}+1\right)}{2^{30}\left(2^{20}+1\right)}\)
\(=\frac{2^{40}}{2^{30}}=2^{10}\)
\(\frac{8^{20}+4^{20}}{4^{25}+64^5}\)
\(=\frac{\left(2^3\right)^{20}+\left(2^2\right)^{20}}{\left(2^2\right)^{25}+\left(2^6\right)^5}\)
\(=\frac{2^{60}+2^{40}}{2^{25}+2^{30}}\)
\(=\frac{2^{40}\left(2^{20}+1\right)}{2^{25}\left(1+2^5\right)}\)
\(=\frac{2^{15}\left(2^{20}+1\right)}{1+2^5}\)
\(=\frac{2^{35}+2^{15}}{1+2^5}\)
\(\frac{8^{14}}{4^{12}}\)
= \(\frac{\left(2^3\right)^{14}}{\left(2^2\right)^{12}}\)
= \(\frac{2^{42}}{2^{24}}\)
= 242 - 24
= 218
\(\frac{8^{14}}{4^{12}}\)\(=\frac{\left(2^3\right)^{14}}{\left(2^2\right)^{12}}\)\(=\frac{2^{42}}{2^{24}}=2^{18}=262144\)