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\(F=\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{9}{4}\right)^9\div\left(\frac{3}{16}\right)^3}{2^7.5^2+512}\)
\(F=\frac{\left(\frac{2.5}{5}\right)^7+\left(\frac{9.16}{4.3}\right)^3}{2^7.5^2+2^9}=\frac{2^7+12^3}{2^7.5^2+2^9}=\frac{2^7+2^6.3^3}{2^7.5^2+2^9}=\frac{2^6.\left(2+3^3\right)}{2^7.\left(5^2+2^2\right)}=\frac{2^6.29}{2^7.29}\)
\(F=\frac{1}{2}\)
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.....\frac{9999}{10000}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}......\frac{99.101}{100.100}\)
\(=\frac{1.2.3...99}{2.3.4....100}.\frac{3.4.5....101}{2.3.4....100}\)
\(=\frac{1}{100}.\frac{101}{2}\)
\(=\frac{101}{200}\)
\(\frac{\left(-2\right)^6\cdot3^7\cdot16}{6^4\cdot2^5\cdot9}\)
\(=\frac{2^6\cdot3^7\cdot2^4}{2^4\cdot3^4\cdot2^5\cdot3^2}\)
\(=\frac{2^{10}\cdot3^7}{2^9\cdot3^6}=2\cdot3=6\)
\(\text{Chúc bạn học tốt !}\)
\(\frac{\left(-2\right)^6.3^7.16}{6^4.2^5.9}\)
\(=\frac{2^6.3^7.2^4}{2^4.3^4.2^5.3^2}\)
\(=\frac{2^{10}.3^7}{2^9.3^6}=2.3=6\)
1: \(\dfrac{-7}{4}\cdot\dfrac{2}{9}=\dfrac{-14}{36}=\dfrac{-7}{18}\)
2: \(=\dfrac{12}{13}\cdot\dfrac{26}{5}=\dfrac{24}{5}\)
3: \(=\dfrac{20}{11}\cdot\dfrac{55}{21}=\dfrac{100}{21}\)
4: \(=\dfrac{-40}{240}=\dfrac{-1}{6}\)
5 . 213 . 411 - 169 / ( 3 . 217)2
=5 . 213 . 222 - 236 / 32.234
=5 . 235 - 236 / 32.234
= 235. (5 - 2) / 32.234
= 235. 3 / 32.234
= 2/3