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20112-(304+2012)+(2013+304)
=20112-304-2012+2013+304
=20112+(-2012+2013)+(-304+304)
=20112+1+0=20113
\(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.25^5.\left(2^3\right)^7}{2^{12}.\left(3^2\right)^{12}.\left(25^2\right)^3.\left(2^3\right)^3.3^3}=\)\(\frac{3^{28}.25^5.2^{21}}{2^{12}.2^9.3^{24}.3^3.25^6}=\frac{3^{28}.25^5.2^{21}}{2^{21}.3^{27}.25^6}\)\(=\frac{3}{25}\)
a) 2012 - ( 304 + 2012 ) + ( 2013 + 304 )
= 2012 - 304 - 2012 + 2013 + 304
= 2012 + ( - 304 ) + ( - 2012 ) + 2013 + 304
= [ 2012 + ( - 2012 ) ] + [ ( - 304 ) + 304 ] + 2013
= 0 + 0 + 2013
= 2013
b) \(\frac{9^{14}.25^5.8^7}{18^{12}.625^3.24^3}\)
\(=\frac{\left(3^2\right)^{14}.\left(5^2\right)^5.\left(2^3\right)^7}{\left(3^2.2\right)^{12}.\left(5^4\right)^3.\left(2^3.3\right)^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{3^{24}.2^{12}.5^{12}.2^9.3^3}\)
\(=\frac{3^{28}.5^{10}.2^{21}}{3^{27}.5^{12}.2^{21}}\)
\(=\frac{3}{5^2}=\frac{3}{25}\)
a) 2012 - ( 304 + 2012 ) + (2013 + 304 )
= 2012 - 304 +2012 + 2013 + 304
= ( 2012 - 2012 ) + ( 304 + 304 ) + 2013
= 0 + 608 + 2013
= 2621
Chờ một chút để minh suy nghĩ
2012 - 304 + 2012 + 2013 + 304
= ( 2012 - 2012 ) + ( 304 - 304 ) + 2013
= 2013 + 0 + 0
= 2013
\(\frac{9^{14}\cdot25^5\cdot8^7}{18^{12}\cdot625^3\cdot24^3}=\frac{\left(3^2\right)^{14}\cdot\left(5^2\right)^5\cdot\left(2^3\right)^7}{\left(3^2\cdot2\right)^{12}\cdot\left(5^4\right)^3\cdot\left(3\cdot2^3\right)^3}\)
\(=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{3^{24}\cdot2^{12}\cdot5^{12}\cdot3^3\cdot2^9}=\frac{3^{28}\cdot5^{10}\cdot2^{21}}{3^{25}\cdot5^{12}\cdot2^{21}}=\frac{3^3}{5^2}=\frac{27}{25}\)
\(\frac{9^{14}}{18^{12}}.\frac{25^5}{625^3}.\frac{8^7}{24^3}\)
\(=\frac{9^{14}}{\left(9.2\right)^{12}}.\frac{25^5}{25^6}.\frac{8^7}{\left(8.3\right)^3}\)
\(=\frac{9^{14}}{9^{12}.2^{12}}.\frac{1}{25}.\frac{8^7}{8^3.3^3}\)
\(=\frac{9^2}{2^{12}}.\frac{1}{25}.\frac{8^4}{3^3}\)
\(=\frac{81}{4096}.\frac{1}{25}.\frac{4096}{27}\)
\(=\frac{81}{4096}.\frac{4096}{27}.\frac{1}{24}=3.\frac{1}{24}=\frac{3}{24}\)
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\(\frac{9^{14}.225^5.8^7}{18^{12}.625^3.24^3}=\frac{\left(3^2\right)^{14}.\left(3^2.5^2\right)^5.\left(2^3\right)^7}{\left(3^2.2\right)^{12}.\left(5^4\right)^3.\left(3.2^3\right)^3}=\frac{3^{28}.3^{10}.5^{10}.2^{21}}{3^{24}.2^{12}.5^{12}.3^3.2^9}=\frac{3^{38}.5^{10}.2^{21}}{3^{27}.2^{21}.5^{12}}=\frac{3^{11}}{5^2}\)
2015-2014+2013-2012+...+9-8+7
= (2015-2014)+(2013-2012)+...+(9-8)+7
= 1+1+...+1+7
=> 1.1004+7
= 1004+7
= 1011
2015-2014+2013-2012+...+9-8+7
= (2015-2014)+(2013-2012)+...+(9-8)+7
= 1+1+...+1+7
=> 1.1004+7
= 1004+7
= 1011
2012-304-2012+2013+304
=(2012-2012)+(304-304)+2013
=0+0+2013
=2013
2012 - ( 304 + 2012 ) + ( 2013 + 304 )
= 2012 - 2316 + 2317
= -304 + 2317
= 2013