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\(\frac{9^{14}.25^5.8^2.8^7}{18^{12}.625^3.24^3}=\frac{3^{28}.5^{10}.8^9}{2^{12}.9^{12}.5^{12}.3^3.2^9}\)\(=\frac{3^{28}.5^{10}.2^{27}}{2^{21}.5^{12}.3^{24}.3^3}=\frac{3^{28}.5^{10}.2^{27}}{2^{21}.5^{12}.3^{27}}\) \(=\frac{3.2^6}{5^2}=\frac{192}{25}=7,68\)
\(a,25< 5^n< 625\Leftrightarrow5^2< 5^n< 5^4\Leftrightarrow2< n< 4\Leftrightarrow n=3\)
Vậy số cần điền là 3
\(b,256>2^n>8^2\Leftrightarrow2^8>2^n>8^2\)
\(\Leftrightarrow2^8>2^n>\left[2^3\right]^2\)
\(\Leftrightarrow2^8>2^n>2^6\Leftrightarrow8>n>6\Leftrightarrow n=7\)
a.87 .914 .255 tren 6253 .1812 .243 =(23 )7 .(32 )14 .(52)5 tren (54 )3 .(2.32 )12 .(23 .3)3 =221 .328 .510 tren 512 .(2.32 )12 .(23 .3)3 =217 .325 tren 52 .1.1=217.325 tren 25.
b.(3.128.216 )2 tren (2.4.8.16.32.64)2 =(3.27 .216 )2 tren (2..22 .23 .24 .25 .26 )2 =(3.223 )2 tren (221 )2 =(3.22 )2 tren 1=122 =144
c.4.312 +5.311 tren 39 .23 -39 .52 =4.311 .3+5.311 tren 39 .(23 -52 )=(4+5).311 .3 tren 39 .(8-25)=9.312 tren 39 .(-17)=32 .312 tren 39 .(-17)=314 tren 39 .(-17)=35 tren -17.
hihi ko bt dung ko nua
\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(2.3^2\right)^{12}.\left(5^4\right)^3.\left(3.2^3\right)^3}=\frac{3^{28}.5^{10}.2^{21}}{2^{12}.3^{24}.5^{12}.3^3.2^9}=\frac{3^{28}.5^{10}.2^{21}}{2^{21}.3^{27}.5^{12}}=\frac{3}{5^2}=\frac{3}{25}\)
a)2/15
c)50/77