Rút gọn phân số : a) M = 9^4.27^5.3^6.3^4/3^8.81^4.234.8^2
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LV
1
HL
2
AK
10 tháng 4 2018
\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.243.8^2}\)
\(M=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.\left(3^5\right).\left(2^3\right)}\)
\(M=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.3^5.8}\)
\(M=\frac{3^{33}}{3^{29}.8}\)
\(M=\frac{3^4}{1.8}\)
\(M=\frac{81}{8}\)
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DP
27 tháng 6 2017
\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.234.8^2}=\frac{\left(3^2\right)^4.\left(3^3\right)^5.3^6.3^4}{3^8.\left(3^4\right)^4.3^5.\left(2^3\right)^2}\)
\(M=\frac{3^8.3^{15}.3^6.3^4}{3^{18}.3^{16}.3^5.2^6}=\frac{81}{64}\)
\(N=\frac{4^6.9^5.6^9.120}{8^4.3^{12}-6^{11}}=\frac{2^{12}.3^{10}+2^{12}.3^{10}.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)
\(N=\frac{2^{12}.3^{10}.\left(1+5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\frac{2.6}{3.5}\)
\(N=\frac{4}{5}\)
15 tháng 1 2018
a ) \(\frac{2.9+6.7}{8.5+4.2}\)
= \(\frac{2.9+2.3.7}{2.2.2.5+4.2}\)
= \(\frac{9+3.7}{2.5+4.2}\)= \(\frac{30}{18}\)= \(\frac{5}{3}\)
DN
15 tháng 1 2018
a, 2.9+6.7/8.5+4.2
=2.3.3+2.3.7/2.4.5+2.4
=2.3.(3+7)/2.4.(5+1)
=30/24
=5/4
b,297-15/1188-60
=282/1128
=1/4
c, 2^5.3^7+2^5.3^2/2^6.3^10
=2^5.(3^7+3^2)/2.2^5.3^10
=3^9/2.3.3^9
=1/6
TN
1
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
12 tháng 5 2022
\(=\dfrac{\left(2^3\right)^3.\left(3^2\right)^4-2^8.\left(3^4\right)^2}{\left(2^4\right)^2.\left(3^4\right)^2+\left(2^2\right)^4.\left(3^3\right)^3}=\dfrac{2^9.3^8-2^8.3^8}{2^8.3^8+2^8.3^9}=\)
\(=\dfrac{2^8.3^8.\left(2-1\right)}{2^8.3^8.\left(1+3\right)}=\dfrac{1}{4}\)
NL
1
H9
HT.Phong (9A5)
CTVHS
18 tháng 10 2023
\(m=\dfrac{2^7\cdot3^5+2^4\cdot3^9}{2^6\cdot3^5+2^3\cdot3^9}\)
\(m=\dfrac{2^4\cdot3^5\cdot\left(2^3+3^4\right)}{2^3\cdot3^5\cdot\left(2^3+3^4\right)}\)
\(m=\dfrac{2^4\cdot3^5}{2^3\cdot3^5}\)
\(m=\dfrac{2^4}{2^3}\)
\(m=2^{4-3}\)
\(m=2\)
Lời giải:
\(M=\frac{9^4.27^5.3^6.3^4}{3^8.81^4.234.8^2}=\frac{(3^2)^4.(3^3)^5.3^6.3^4}{3^8.(3^4)^4.2.3^2.13.(2^3)^2}\)
\(=\frac{3^8.3^{15}.3^6.3^4}{3^8.3^{16}.2.3^2.13.2^6}=\frac{3^{33}}{3^{26}.2^7.13}=\frac{3^7}{2^7.13}\)