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a)0,310=(0,32)10=0,910
0,9>0,1=>0,910>0,110hay0,320>0,110
b)430+320=(43)10+(32)10=(43+32)10=7310
3.24=72
có 73>72 => 7310>7210 hay 430+320>3.2410 (câu này mình ko chắc đúng đâu)
a: \(=\left(\dfrac{-1}{3}:\dfrac{-2}{3}\right)^3+\left(\dfrac{4}{21}\cdot\dfrac{21}{4}\right)^{50}+0.01\)
\(=\left(\dfrac{1}{2}\right)^3+1^{50}+0.01=0.125+1+0.01=1.135\)
b: \(=x:y+\left(\dfrac{2x}{y}\right)^2-11x+12x-12y\)
\(=\dfrac{x}{y}+\dfrac{4x^2}{y^2}+x-12y\)
\(=\dfrac{x^2+4x^2+xy^2-12y^3}{y^2}=\dfrac{5x^2+xy^2-12y^3}{y^2}\)
\(a,\left(1+3x\right)^2=1+6x+9x^2\)
\(b,\left(2a^2+b^2\right)^2=4a^4+4a^2b^2+b^4\)
\(c,\left(\frac{x}{2}-2y\right)^2=\frac{x^2}{4}-2xy+4y^2\)
\(d,\left(x^2-0,1\right)^2=x^4-0,2x+0,01\)
\(e,\left(2x-3\right)\left(2x+3\right)=4x^2-9\)
\(g,\left(a^2+5\right)\left(5-a^2\right)=25-a^4\)
\(h,39.41=\left(40-1\right)\left(40+1\right)=40^2-1=1599\)
a) \(\left(1+3x\right)^2=1+6x+9x^2\)
b) \(\left(2a^2+b^2\right)^2=4a^4+4a^2b^2+b^4\)
c) \(\left(\frac{x}{2}-2y\right)^2=\frac{x^2}{4}-2xy+4y^2\)
d) \(\left(x^2-0,1\right)^2=x^4-0,2x^2+0,01\)
e) \(\left(2x-3\right)\left(2x+3\right)=\left(2x\right)^2-3^2=4x^2-9\)
g) \(\left(a^2+5\right)\left(5-a^2\right)=25-a^4\)
\(-0,00001=\left(-0,1\right)^x.\)
\(\Leftrightarrow-\frac{1}{100000}=\left(-\frac{1}{10}\right)^x\)
\(\Leftrightarrow\left(-\frac{1}{10}\right)^5=\left(-\frac{1}{10}\right)^x\)
\(\Rightarrow x=5\)
Ta có: \(\left(\frac{1}{16}\right)^{10}=\left(\frac{1}{2^4}\right)^{10}=\frac{1}{2^{40}}\)
\(\left(\frac{1}{2}\right)^{50}=\frac{1}{2^{50}}\)
Vì \(2^{40}< 2^{50}\Rightarrow\frac{1}{2^{40}}>\frac{1}{2^{50}}\)hay \(\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)
Ta có: \(\left(0,3\right)^{20}=\left[\left(0,3\right)^2\right]^{10}=\left(0,09\right)^{10}\)
Vì \(0,09< 0,1\Rightarrow\left(0,09\right)^{10}< \left(0,1\right)^{100}\)
hay \(\left(0,3\right)^{20}< \left(0,1\right)^{10}\)
Ta có :
\(0,1< 0,3\Rightarrow\left(0,1\right)^{10}< \left(0,3\right)^{10}\)
Vậy \(\left(0,1\right)^{10}< \left(0,3\right)^{10}\)
\(\left(0,1\right)^4.\left(0,1\right)^2.10^4\)
\(=\frac{1}{10^4}.10^4.\frac{1}{10^2}\)
\(=1.\frac{1}{100}=\frac{1}{100}\)
Ta có :
(0,1)4 x (0,1)2 x 104
=( 0,1 x 10)4 x 0,01
= 14 x 0,01
= 0,01