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11 tháng 9 2019
\(a,\frac{(-10)^5}{3\cdot(-6)^4}=\frac{(-2\cdot5)^5}{3\cdot(-2\cdot3)^4}=\frac{(-2)^5\cdot5^5}{3\cdot(-2)^4\cdot3^4}=\frac{(-2)^5\cdot5^5}{(-2)^4\cdot3^5}=-2\cdot\frac{5^5}{3^5}=\frac{-6250}{243}\)
\(b,\frac{2^{15}\cdot9^4}{6^6\cdot8^3}=\frac{\left[2^3\right]^5\cdot\left[3^2\right]^4}{\left[3\cdot2\right]^6\cdot\left[2^3\right]^3}=\frac{2^{15}\cdot3^8}{3^6\cdot2^6\cdot2^9}=\frac{2^{15}\cdot3^8}{3^6\cdot2^{15}}=\frac{3^8}{3^6}=3^2=9\)
\(c,\left[1+\frac{2}{3}-\frac{1}{4}\right]\cdot\left[\frac{4}{5}-\frac{3}{4}\right]^2\)
\(=\left[\frac{12}{12}+\frac{8}{12}-\frac{3}{12}\right]\cdot\left[\frac{16}{20}-\frac{15}{20}\right]^2\)
\(=\frac{17}{12}\cdot\left[\frac{1}{20}\right]^2=\frac{17}{12}\cdot\frac{1^2}{20^2}=\frac{17}{12}\cdot\frac{1}{400}=\frac{17}{4800}\)
\(d,2^3+3\cdot\left[\frac{1}{2}\right]^0+\left[(-2)^2:\frac{1}{2}\right]\)
\(=8+3\cdot\frac{1^0}{2^0}+\left[4:\frac{1}{2}\right]\)
\(=8+3\cdot1+8=8+3+8=19\)
16 tháng 10 2022
a: \(\Leftrightarrow4^x\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)=4^8\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)\)
=>4^x=4^8
=>x=8
b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)
=>2^x=2^11
=>x=11
c: =>1/6*6^x+6^x*36=6^15(1+6^3)
=>6^x=6*6^15
=>x=16
d: \(\Leftrightarrow8^x\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)=8^9\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)\)
=>x=9
14 tháng 8 2017
a, \(4^3.5^3=\left(4.5\right)^3=20^3=8000\)
b, \(6^3.5^3=\left(6.5\right)^3=30^3=27000\)
c, \(8^2.5^2=\left(8.5\right)^2=40^2=1600\)
d, \(125^3.8^3=\left(125.8\right)^3=1000^3\)
e, \(5^2.6^2.3^2=\left(5.6.3\right)^2=90^2\)
HN
0
HT
1
22 tháng 5 2022
\(A=\dfrac{3^6\cdot3^8\cdot5^4-5^{13-9}\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6\cdot2}\)
\(=\dfrac{3^{13}\cdot5^4\cdot2}{3^{12}\cdot5^6\cdot2}=\dfrac{3}{25}\)
\(B=\left(\dfrac{2}{5}\cdot5\right)^7+\left(\dfrac{9}{4}:\dfrac{3}{16}\right)^3=1+12^3=1729\)
28 tháng 2 2022
c: \(=\dfrac{7}{23}\cdot\left(\dfrac{-4}{3}-\dfrac{5}{2}\right)=\dfrac{7}{23}\cdot\dfrac{-8-15}{6}\)
\(=\dfrac{7}{23}\cdot\dfrac{-23}{6}=-\dfrac{7}{6}\)
d: \(=\dfrac{5}{7}\left(23+\dfrac{1}{4}-13-\dfrac{1}{4}\right)=\dfrac{5}{7}\cdot10=\dfrac{50}{7}\)
e: \(=\dfrac{2^5\cdot3^3\cdot5^3}{2^3\cdot3^3\cdot2^2\cdot5^2}=5\)
i: \(=\dfrac{1}{3^{10}}\cdot3^{50}-\dfrac{2^{10}}{3^{10}}:\dfrac{4^5}{3^{10}}\)
\(=3^{40}-1\)
DH
25 tháng 6 2017
a, \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{4^5}{2^{10}}=\dfrac{\left(2^2\right)^5}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)
b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)
c, \(\dfrac{9^7.5^6.125^9}{15^{15}.5^{18}}=\dfrac{3^{21}.5^6.5^{27}}{5^{15}.3^{15}.5^{18}}=\dfrac{3^{21}.5^{33}}{3^{15}.5^{33}}=3^6=729\)
d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(=\dfrac{2^{12}.3^9.\left(1+3.5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.16}{3^2.5}=\dfrac{32}{45}\)
Chúc bạn học tốt!!!
26 tháng 2 2022
c: \(=\dfrac{7}{23}\cdot\dfrac{-24-45}{18}=\dfrac{7}{23}\cdot\dfrac{-69}{18}=\dfrac{7}{18}\cdot\left(-3\right)=-\dfrac{7}{6}\)
d: \(=\dfrac{7}{5}\left(23+\dfrac{1}{4}-13-\dfrac{1}{4}\right)=\dfrac{7}{5}\cdot10=14\)
e: \(=\dfrac{2^5\cdot3^3\cdot5^3}{2^3\cdot3^3\cdot2^2\cdot5^2}=5\)
i: \(=\dfrac{1}{3^{10}}\cdot3^{50}-\dfrac{2^{10}}{3^{10}}:\dfrac{4^5}{9^5}=3^{40}-1\)
a) \(\frac{2^{15}.9^4}{6^6.8^3}=9\)
Tk và nhé ^-^
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