\(A=\dfrac{27^3.54^2}{108^4}\)
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28 tháng 5 2022
\(A=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(2^2\cdot3^3\right)^4}=\dfrac{2^9\cdot3^6\cdot2^2\cdot3^6}{2^8\cdot3^{12}}=2^3=8\)
21 tháng 8 2021
\(\dfrac{72^3.54^2}{108^4}\)
\(=\dfrac{18^3.4^3.18^2.3^2}{18^4.6^4}\)
\(=\dfrac{18^5.2^6.3^2}{18^4.2^4.3^4}\)
\(=\dfrac{18.2^2}{3^2}\)
\(=\dfrac{9.2.2^2}{9}\)
\(=2^3=8\)
FC
25 tháng 10 2018
a, \(B=\dfrac{2^{10}.13+2^{10}.65}{2^8.104}\)
\(=\dfrac{2^{10}.\left(13+65\right)}{2^8.2^3.13}\)
\(=\dfrac{2^{10}.78}{2^{11}.13}\)\(=\dfrac{1.6}{2.1}=\dfrac{1.3}{1.1}=3\)
29 tháng 10 2022
b: \(=\dfrac{2^{20}\cdot3^2+2^{54}}{2^{18}\cdot5^2}=\dfrac{2^{20}\left(3^2+2^{32}\right)}{2^{18}\cdot5^2}=\dfrac{2^2\left(3^2+2^{32}\right)}{25}\)
c: \(=\dfrac{2^9\cdot3^6\cdot3^6\cdot2^2}{2^8\cdot3^{12}}=\dfrac{2^{11}}{2^8}=8\)
d: \(=\dfrac{2^{12}\cdot3^4\cdot3^{10}}{2^{12}\cdot3^{12}}=9\)
12 tháng 10 2018
\(A=\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=\dfrac{2^{11}.3^{12}}{2^8.3^{12}}=2^3=8\)
\(B=\dfrac{3^{11}.11+3^{10}.5}{3^{10}.\left(11+5\right)}=\dfrac{3^{10}\left(3.11+5\right)}{3^{10}\left(11+5\right)}=\dfrac{38}{16}=\dfrac{19}{8}\)
15 tháng 7 2017
a) \(\frac{6^{10}.27^5}{4^5.81^6}=\frac{\left(2.3\right)^{10}.\left(3^3\right)^5}{\left(2^2\right)^5.\left(3^4\right)^6}=\frac{2^{10}.3^{10}.3^{15}}{2^{10}.3^{24}}=\frac{2^{10}.3^{25}}{2^{10}.3^{24}}=\frac{3^{25}}{3^{24}}=3\)
b) \(\frac{72^3.54^2}{108^4}=\frac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}=\frac{2^9.3^6.2^2.3^6}{2^8.3^{12}}=\frac{2^{11}.3^{12}}{2^8.3^{12}}=\frac{2^{11}}{2^8}=2^3=8\)
c) \(\frac{27^4.2^3-3^{10}.4^3}{6^4.9^3.4}=\frac{\left(3^3\right)^4.2^3-3^{10}.\left(2^2\right)^3}{\left(2.3\right)^4.\left(3^2\right)^3.2^2}=\frac{3^{12}.2^3-3^{10}.2^6}{2^4.3^4.3^6.2^2}\)
= \(\frac{3^{12}.2^3-3^{10}.2^6}{2^6.3^{10}}=\frac{3^{12}.2^3}{2^6.3^{10}}-\frac{3^{10}.2^6}{2^6.3^{10}}=\frac{3^2}{2^3}-1=\frac{9}{8}-1=\frac{1}{8}\)
KL
31 tháng 7 2017
a, (0,25)3.32
= 0,5
b, \(\dfrac{72^3.54^2}{108^4}=\dfrac{\left(2^3.3^2\right)^3.\left(2.3^3\right)^2}{\left(2^2.3^3\right)^4}\)\(=\dfrac{2^9.3^6.2^2.3^6}{2^8.3^{12}}\)
\(=\dfrac{2^{11}.3^{12}}{2^8.3^{12}}=2^3\)
c, \(\dfrac{81^{11}.3^{17}}{27^{10}.9^{15}}=\dfrac{\left(3^4\right)^{11}.3^{17}}{\left(3^3\right)^{10}.\left(3^2\right)^{15}}=\dfrac{3^{44}.3^{17}}{3^{30}.3^{30}}\)\(=\dfrac{3^{61}}{3^{60}}=3\)
@Lớp 6B Đoàn Kết
MM
1
28 tháng 11 2016
a)4^10x8^15=(2^2)10x(2^3)15
=22x10x23x15
= 220x245
=220+45
=265
5 tháng 7 2018
\(A=\dfrac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}=\dfrac{3^{10}\cdot\left(11+5\right)}{3^9\cdot16}=\dfrac{3^{10}\cdot16}{3^9\cdot16}=3\)
\(B=\dfrac{2^{10}\cdot13+2^{10}\cdot65}{2^8\cdot104}=\dfrac{2^{10}\cdot\left(13+65\right)}{2^8\cdot2^2\cdot26}=\dfrac{2^{10}\cdot78}{2^{10}\cdot26}=3\)
\(C=\dfrac{72^3\cdot54^2}{108^4}=\dfrac{\left(2^3\cdot3^2\right)^3\cdot\left(2\cdot3^3\right)^2}{\left(3^3\cdot2^2\right)^4}\\ =\dfrac{2^9\cdot3^6\cdot2^4\cdot3^6}{3^{12}\cdot2^8}=\dfrac{2^{13}\cdot3^{12}}{3^{12}\cdot2^8}=2^5=32\)
\(D=\dfrac{11\cdot3^{22}\cdot3^7-9^{15}}{\left(2\cdot3^{14}\right)^2}=\dfrac{11\cdot3^{29}-\left(3^2\right)^{15}}{2^2\cdot3^{28}}=\dfrac{11\cdot3^{29}-3^{30}}{2^2\cdot3^{28}}\\ =\dfrac{3^{29}\cdot\left(11-3\right)}{2^2\cdot3^{28}}=\dfrac{3^{29}\cdot8}{4\cdot3^{28}}=3\cdot2=6\)
\(A=\dfrac{27^3.54^2}{108^4}\)
\(=\dfrac{\left(3^3\right)^3.\left(3^3.2\right)^2}{\left(2^2.3^3\right)^4}\)
\(=\dfrac{3^9.3^6.2^2}{2^8.3^{12}}\)
\(=\dfrac{3^{15}.2^2}{2^8.3^{12}}\)
\(=\dfrac{3^3}{2^5}=\dfrac{27}{32}\)
Vậy A =\(\dfrac{27}{32}\)
\(\dfrac{3^3}{2^6}=\dfrac{27}{64}\)
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