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a, Xét : \(\left(2x-1\right)^4=1\Leftrightarrow\orbr{\begin{cases}2x-1=1\\2x-1=-1\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=0\end{cases}}}\)
Xét : \(\left(81.2\right)\left(x-2\right)^2=1\Leftrightarrow162\left(x-2\right)^2=1\Leftrightarrow\left(x-2\right)^2=\frac{1}{162}\)
\(\orbr{\begin{cases}x-2=\sqrt{\frac{1}{162}}\\x-2=-\sqrt{\frac{1}{162}}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\frac{36+\sqrt{2}}{18}\\x=\frac{36-\sqrt{2}}{18}\end{cases}}\)
\(a,35:\left(\frac{-5}{3}\right)+2\frac{1}{2}:\left(-\frac{5}{3}\right)=35.\left(-\frac{3}{5}\right)+\frac{5}{2}.\left(-\frac{3}{5}\right)\)
\(=-21+-\frac{3}{2}\)
\(=\frac{-42-3}{2}=-\frac{45}{2}\)
\(b,\frac{10^3+2.5^3+5^3}{55}=\frac{\left(2.5\right)^3+2.5^3+5^3}{5.11}\)
\(=\frac{5^3\left(2^3+2+1\right)}{5.11}\)
\(=\frac{5^2\left(8+2+1\right)}{11}\)
\(=\frac{5^2.11}{11}=5^2=25\)
\(C,\frac{27^2.2^5}{6^6.32^3}=\frac{\left(3^3\right)^2.2^5}{\left(2.3\right)^6.2^5}\)
\(=\frac{3^6}{2^6.3^6}=\frac{1}{2^6}=\frac{1}{64}\)
Ta có : \(A=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^5}+.....+\frac{1}{2^{99}}\)
\(\Rightarrow2^2A=2+\frac{1}{2}+\frac{1}{2^3}+.....+\frac{1}{2^{97}}\)
\(\Rightarrow4A-A=2-\frac{1}{2^{99}}\)
\(\Rightarrow3A=2-\frac{1}{2^{99}}\)
\(\Rightarrow A=\frac{2-\frac{1}{2^{99}}}{3}\)
B1:
a)x=-3/5*9/25 =>x=-27/125
b)x=(4/7)6:(4/7)4 =>x=(4/7)2=16/49
c)(x/4)2=4:(x/2)
(x/4)2=8/x
x2/16=8/x2
x3=128
x=5,039
B2
M=23.10+22.10/23.4+22.11
=230+220/212+222
=230+28+222
=28(222+1+214)
=2
1.1
x=(3/5)^7:(3/5)^5=(3/5)^7-5=(3/5)62=6/5=1,2
1.2
x=5+7/10+3/10=5+10/10=5+1=6
1.3
x=\(\frac{18}{23}\) :\(\frac{6}{7}\) =\(\frac{18}{23}\) . \(\frac{7}{6}\) = \(\frac{21}{23}\)