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a) \(15\cdot5+75\cdot5+5\cdot3+5\cdot7\)
\(=5\left(15+75\right)+5\left(3+7\right)\)
\(=5\cdot90+5\cdot10=5\left(90+10\right)=5\cdot100=500\)
b) \(2\cdot200+4\cdot200+4\cdot50+125\cdot8\)
\(=2.2.100+4\cdot200+4\cdot50+125\cdot2\cdot4\)
\(=4\left(100+200+50+250\right)\)
\(=4\cdot600=2400\)
c) \(125\cdot20\cdot80\cdot2\cdot100\cdot5\)
\(=\left(125\cdot8\right)\cdot\left(2\cdot5\right)\cdot100\cdot20\)
\(=1000\cdot10\cdot100\cdot20\)
\(=20000000\)
21*7^2 -11*7^2 +90*7^2 +49*125*16
=7^2* ( 21 -11+ 90 ) + 7^2* 2000
=7^2* 100 + 7^2* 2000
=7^2* ( 100+ 2000 )
=49*2100
=102900
\(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{3^2.5^{20}.3^{27}-3.3^{30}.5^{18}}{7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}}\)
\(=\frac{3^{29}.5^{18}.5^2-3^2.3^{29}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{18}.5}\)
\(=\frac{3^{29}.5^{18}.\left(5^2-3^2\right)}{3^{29}.5^{18}.\left(7-5\right)}\)
\(=\frac{25-9}{2}\)
\(=\frac{16}{2}=8\)
5/7-4/19+2/7-15/19-1999/2006=(5/7+2/7)-(4/19+15/19)-1999/2006
=1-1-1999/2006=0-1999/2006=-1999/2006
30000
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