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NL
0
VH
1
23 tháng 8 2023
\(\dfrac{8^2.125.9^2-32.5^3.81}{20^3.3^4-6^8.5^4}\)
\(=\dfrac{2^6.5^3.3^4-2^5.5^3.3^4}{4^3.5^3.3^4-2^8.3^8.5^4}\)
\(=\dfrac{2^6.5^3.3^4-2^5.5^3.3^4}{2^6.5^3.3^4-2^8.3^8.5^4}\)
\(=\dfrac{2^5.5^3.3^4\left(2-1\right)}{2^6.5^3.3^4\left(1-2^2.3^4.5\right)}\)
\(=\dfrac{2^5.5^3.3^4.1}{2^6.5^3.3^4\left(1-810\right)}\)
\(=\dfrac{1}{2.\left(-809\right)}\)
\(=-\dfrac{1}{1618}\)
5 tháng 7 2023
1: =1/8*9/4=9/32
2: =8/27*243/32=9/4
3: =(5/4*4/5)^5*(4/5)^2=16/25
4: \(=\left(-\dfrac{5}{6}\cdot\dfrac{6}{5}\right)^2\cdot\left(\dfrac{6}{5}\right)^2=\dfrac{36}{25}\)
5: \(=\left(-\dfrac{4}{3}\right)^3\cdot\left(\dfrac{3}{4}\right)^{10}=\left(-1\right)\left(\dfrac{3}{4}\right)^7=-\left(\dfrac{3}{4}\right)^7\)
6: \(=\left(\dfrac{1}{3}\cdot\dfrac{-9}{2}\right)^4\left(-\dfrac{9}{2}\right)^2=\left(-\dfrac{3}{2}\right)^4\cdot\dfrac{81}{4}=\dfrac{9}{4}\cdot\dfrac{81}{4}=\dfrac{729}{16}\)
8: =(0,2*5)^4*5^2=25
10: =-0,5^5*2^10
=-0,5^5*2^5*2^5
=-32
13: =(0,5*2)^2*2^2=4
DN
4
4 tháng 2 2020
\(\frac{2^{12}.3^5-4^6.81}{\left[\left(2^2.3\right)^6+8^4.3^5\right]}=\frac{2^{12}.3^5-\left(2^2\right)^6.3^4}{2^{12}.3^6+\left(2^3\right)^4.3^5}\)
\(=\frac{2^{12}.3^5-2^{12}.3^4}{2^{12}.3^6-2^{12}.3^5}=\frac{2^{12}\left(3^5-3^4\right)}{2^{12}\left(3^6-3^5\right)}\)
\(=\frac{3^4\left(3-1\right)}{3^5\left(3-1\right)}=\frac{1}{3}\)
NM
1
11 tháng 2 2020
\(\frac{2^{12}\cdot3^5-4^6\cdot81}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}=\frac{2^{12}\cdot3^5-\left(2^2\right)^6\cdot3^4}{2^{12}\cdot3^6+\left(2^3\right)^4\cdot3^5}\)
\(=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}\)
\(=\frac{2^{12}\left(3^5-3^4\right)}{2^{12}\left(3^6+3^5\right)}=\frac{3^5-3^4}{3^6+3^5}\)
\(=\frac{3^4\left(3-1\right)}{3^5\left(3+1\right)}=\frac{3^4\cdot2}{3^5\cdot4}=\frac{3^4\cdot2}{3^4\cdot3\cdot4}=\frac{2}{3\cdot4}\)
\(=\frac{1}{3\cdot2}=\frac{1}{6}\)