27 (x-64)=81
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43 x 27 + 93 x 43 + 57 x 61 + 59 x 57
= 43 x ( 27 + 93 ) + 57 x ( 61 + 59 )
= 43 x 120 + 57 x 120
= 120 x ( 43 + 57 )
= 120 x 100
= 1200
b) 64 x 6 + 81 x 4 + 17 x 6
= 6 x ( 64 + 17 ) + 81 x 4
= 6 x 81 + 81 x 4
= 81 x ( 6 + 4 )
= 81 x 10
= 810
A) =43 x (27+93)+57*(61+59)
=43*120+57*120
=120*(43+57)
=120*100
=12000
a, 410. 230=220.230=250
b,925.274.813= 350.312.312=374
Tương tự các câu khác....
a, 410.230 = (22)10.230 = 220.230 = 250
b, 925.274.813 = (32)25.(33)4.(34)3 = 350.312.312 = 374
c, 2550.1255 = (52)50.(53)5 = 5100.515 = 5115
d, 643.48.164 = (26)3.(22)8.(24)4 = 218.216.216 = 250
e, 38 : 36 = 32
210 : 83 = 210 : (23)3 = 210 : 29 = 2
127 : 67 = (12 : 6)7 = 27
@Dương Tuyết Mai
Bạn để ý: 81 = 3^4 (34) 27 = 3^3
64 = 2^6 256 = 2^8
Vậy \(\left(\frac{27}{64}\right)^{15}=\left(\frac{3^2}{8^2}\right)^{15}=\left(\frac{3}{8}\right)^{30};\left(\frac{81}{256}\right)^{10}=\left(\frac{3^4}{4^4}\right)^{10}=\left(\frac{3}{4}\right)^{40}\)
Vì 3/8 <3/4 ; 30<40 nên \(\left(\frac{3}{8}\right)^{30}
a) \(\frac{1}{27}.81^n=3^n\)\(\Leftrightarrow81^n=3^n.27\)
\(\Leftrightarrow3^{4n}=3^n.3^3=3^{n+3}\)\(\Leftrightarrow4n=n+3\)
\(\Leftrightarrow3n=3\)\(\Leftrightarrow n=1\)( thoả mãn n nguyên dương )
Vậy \(n=1\)
b) \(8< 2^n< 64\)\(\Leftrightarrow2^3< 2^n< 2^6\)\(\Leftrightarrow3< n< 6\)
Vì n nguyên dương \(\Rightarrow n\in\left\{4;5\right\}\)
Vậy \(n\in\left\{4;5\right\}\)
\(\left(x+1\right)^2=81\)
\(\Rightarrow\left(x+1\right)^2=9^2\)
\(\Rightarrow x+1=9\)
\(\Rightarrow x=9-1=8\)
Vậy x = 8
b, \(\left(x+5\right)^3=-64\)
\(\Rightarrow\left(x+5\right)^3=\left(-4\right)^3\)
\(\Rightarrow x+5=-4\)
\(\Rightarrow x=\left(-4\right)-5\)
\(\Rightarrow x=-9\)
Vậy x = -9
c, \(\left(2x-3\right)^2=9\)
\(\Rightarrow\left(2x-3\right)^2=3^2\)
\(\Rightarrow2x-3=3\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
Vậy x = 3
d, \(\left(4x+1\right)^3=27\)
\(\Rightarrow\left(4x+1\right)^3=3^3\)
\(\Rightarrow4x+1=3\)
\(\Rightarrow4x=2\)
\(\Rightarrow x=\frac{1}{2}\)
Vậy x = \(\frac{1}{2}\)
\(a,27^4\cdot81^{10}=\left(3^3\right)^4\cdot\left(3^4\right)^{10}=3^{12}\cdot3^{40}=3^{52}\\ b,=8^{31}\cdot32^5:64^4=\left(2^3\right)^{31}\cdot\left(2^5\right)^5:\left(2^6\right)^4=2^{93}\cdot2^{25}:2^{24}=2^{93+25-24}=2^{94}\)
x-64=81/27
x-64=3
x=3+64
x=67
x-64=81:27 x-6=3 x =3+64 x =67