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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) \(125\cdot20\cdot80\cdot2\cdot100\cdot5\)
\(=\left(125\cdot8\right)\cdot\left(2\cdot5\right)\cdot100\cdot20\)
\(=1000\cdot10\cdot100\cdot20\)
\(=20000000\)
\(46\cdot99\)
\(=46\cdot\left(100-1\right)\)
\(=46\cdot100-46\)
\(=4600-46\)
\(=4554\)
___________
\(34\cdot11\)
\(=34\cdot\left(10+1\right)\)
\(=34\cdot10+34\)
\(=340+34\)
\(=374\)
___________
\(25\cdot12\)
\(=5\cdot5\cdot12\)
\(=5\cdot60\)
\(=300\)
__________
\(15\cdot4\)
\(=15\cdot2\cdot2\)
\(=30\cdot2\)
\(=60\)
____________
\(45\cdot6\)
\(=45\cdot2\cdot3\)
\(=90\cdot3\)
\(=2700\)
________
\(13\cdot99\)
\(=13\cdot\left(100-1\right)\)
\(=13\cdot100-13\)
\(=1300-13\)
\(=1287\)
______________
\(16\cdot19\)
\(=16\cdot\left(20-1\right)\)
\(=16\cdot20-16\)
\(=320-16\)
\(=304\)
_____________
\(35\cdot98\)
\(=35\cdot\left(100-2\right)\)
\(=35\cdot100-35\cdot2\)
\(=3500-70\)
\(=3430\)
____________
\(125\cdot16\)
\(=125\cdot8\cdot2\)
\(=1000\cdot2\)
\(=2000\)
___________
\(47\cdot101\)
\(=47\cdot\left(100+1\right)\)
\(=47\cdot100+47\)
\(=4700+47\)
\(=4747\)
46 x 99 =4554 , 34 x 11 = 374 , 25 x 12 =- 300 , 15 x 4 = 60 , 45 x 6 = 270 , 13 x 99 = 1287 , 16 x 19 = 304
35 x 98 = 3430 , 125 x 16 = 2000 , 47 x 101 = 4747
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
\(\frac{9.5^{20}.27^9-3.9^{15}.25^9}{7.3^{29}.125^6-3.3^9.15^{19}}\)
\(=\frac{3^2.5^{20}.3^{27}-3.3^{30}.5^{18}}{7.3^{29}.5^{18}-3^{10}.3^{19}.5^{19}}\)
\(=\frac{3^{29}.5^{18}.5^2-3^2.3^{29}.5^{18}}{7.3^{29}.5^{18}-3^{29}.5^{18}.5}\)
\(=\frac{3^{29}.5^{18}.\left(5^2-3^2\right)}{3^{29}.5^{18}.\left(7-5\right)}\)
\(=\frac{25-9}{2}\)
\(=\frac{16}{2}=8\)
30000
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