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\(\frac{27^2.15^3.125^{17}.10^{10}.3^8.512+1024.25^{28}.12^6.15^7}{125.6^{17}+625^{12}.6^{13}.125^2.25^5.16}\)
=\(\frac{3^6.3^3.5^3.5^{34}.2^{10}.5^{10}.3^8.2^9+2^{10}.5^{56}.3^6.2^{12}.3^7.5^7}{5^{63}.6^{17}+5^{48}.6^{13}.5^6.2^4}\)=\(\frac{3^{17}.5^{47}.2^{19}+2^{22}.5^{63}.3^{13}}{5^{63}.6^{17}+5^{48}.6^{13}.5^6.2^4}=\frac{3^{13}.5^{47}.2^{19}.3^4+2^{19}.5^{47}.3^{13}.2^3.5^{16}}{5^{54}.6^{13}.5^9+5^{54}.6^{13}.2^4}\)
=\(\frac{3^{13}.5^{47}.2^{19}\left(3^4+2^3.5^{16}\right)}{5^{54}.6^{13}\left(5^9+2^4\right)}=\frac{6^{13}.2^6.5^{47}\left(3^4+2^3.5^{16}\right)}{5^7.5^{47}.6^{13}\left(5^9+2^4\right)}=\frac{2^6\left(3^4+2^3.5^{16}\right)}{5^7\left(5^9+2^4\right)}\)
Bạn hãy tự giải nốt
Bạn Hương có 27 viên bi, bạn Hiền có số bi bằng 1/3 số bi của bạn Hương. Trung bình cộng số bi của hai bạn là bao nhiêu?
10 điểm
36 viên
15 viên
30 viên
18 viên
a) \(\dfrac{27^3\cdot11+9^5\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^9\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(=\dfrac{3^9\cdot\left(11+3\cdot5\right)}{3^9\cdot2^4}\)
\(=\dfrac{11+15}{16}\)
\(=\dfrac{26}{16}\)
\(=\dfrac{13}{8}\)
b) \(\dfrac{5^8+2^2\cdot25^4+2^3\cdot125^3-15^4\cdot5^4}{4^2\cdot625^2}\)
\(=\dfrac{5^8+2^2\cdot5^8+2^3\cdot5^9-3^4\cdot5^4\cdot5^4}{2^4\cdot5^8}\)
\(=\dfrac{5^8\cdot\left(1+2^2+2^3\cdot5-3^4\right)}{5^8\cdot2^4}\)
\(=\dfrac{1+4+40-81}{16}\)
\(=\dfrac{-36}{16}\)
\(=\dfrac{-9}{4}\)
c) \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^{10}\cdot3^8\cdot5}\)
\(=\dfrac{2^{10}\cdot3^8\cdot\left(1-3\right)}{2^{10}\cdot3^8\cdot\left(1+5\right)}\)
\(=\dfrac{-2}{6}\)
\(=-\dfrac{1}{3}\)
ta có
\(\frac{3^6.\left(3.5\right)^8}{\left(3.3\right)^7.5^9}\)= \(\frac{3^6.3^8.5^8}{3^7.3^7.5^9}\)= \(\frac{1}{5}\)
Đặt \(A=\frac{3^6.15^8}{9^7.5^9}\)
\(\Leftrightarrow A=\frac{3^6.\left(3.5\right)^8}{\left(3^2\right)^7.5^9}\)
\(\Leftrightarrow A=\frac{3^6.3^8.5^8}{3^{14}.5^9}\)
\(\Leftrightarrow A=\frac{3^{14}.5^8}{3^{14}.5^9}\)
\(\Leftrightarrow A=\frac{3^{14}}{3^{14}}.\frac{5^8}{5^9}\)
\(\Leftrightarrow A=1.\frac{1}{5}=\frac{1}{5}\)
a: \(\left(0.5\right)^3\cdot2^3=1\)
b: \(\left(0.25\right)^2\cdot16=1\)
c: \(\left(\dfrac{3}{5}\right)^3:\left(-\dfrac{27}{1000}\right)=\dfrac{3^3}{5^3}\cdot\dfrac{-1000}{27}=\dfrac{-1000}{125}=-8\)
\(\frac{27^2.25^3}{6.15^4.18}=\frac{\left(3^3\right)^2.\left(5^2\right)^3}{2.3.\left(3.5\right)^4.2.3^2}\)
\(=\frac{3^6.5^6}{2^2.3^7.5^4}=\frac{5^2}{2^2.3}\)
\(=\frac{25}{12}\)