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a, 227 = 23.9 = ( 23)9 = 89
318 = 32.9 = ( 32)9 = 99
b, Ta thấy 8 < 9 nên 227 < 318
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\(2^2+4^2+...+20^2\)
\(=\left(1.2\right)^2+\left(2.2\right)^2+...+\left(2.10\right)^2\)
\(=1^2.2^2+2^2.2^2+...+2^2+10^2\)
\(=2^2.\left(1^2+2^2+3^2+...+10^2\right)\)
\(=4.385\)
\(=1540\)
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a)\(27^6:9^3=\left(3^3\right)^6:\left(3^2\right)^3=3^{18}:3^6=3^{12}\)
b)\(24^n:2^{2n}=\left(2^3.3\right)^n:2^{2n}=2^{3n}.3^n:2^{2n}=2^{3n-2n}.3^n=2^n.3^n=6^n\)
c)\(32^4:8^6=\left(2^5\right)^4:\left(2^3\right)^6=2^{20}:2^{18}=2^2\)
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ta có:A=\(\frac{-3}{2^2}.\frac{-8}{3^2}....\frac{-9999}{100^2}\)
A có 99 thừa số âm
=>A<0
\(=>-A=\frac{3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{99.101}{100.100}\)
=>\(-A=\frac{101}{100.2}=\frac{101}{200}>\frac{100}{200}=\frac{1}{2}=>-A>\frac{1}{2}=>A<-\frac{1}{2}\)
tick nhé
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\(\frac{4^{20}.20^{10}}{80^{10}.5^7}\)\(=\frac{4^{10}.4^{10}.20^{10}}{4^{10}.20^{10}.5^7}\)\(=\frac{4^{10}}{5^7}\)
\(\frac{9^{10}.6^3}{36^7.3^2}\)\(=\frac{3^5.3^2.3^{10}.6^3}{6^3.6^4.6^7.3^2}\)\(=\frac{3^{15}}{6^{11}}\)\(=\frac{3^{11}.3^4}{3^{11}.2^{11}}\)\(=\frac{3^4}{2^{11}}\)
Ta có: \(27\cdot\left(-\dfrac{1}{3}\right)^3+\dfrac{1}{2}\cdot\sqrt{4}\)
\(=27\cdot\dfrac{-1}{27}+\dfrac{1}{2}\cdot2\)
=-1+1
=0