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1) $(-81)\cdot27-3^4\cdot(-77)$
$=(-81)\cdot27-81\cdot(-77)$
$=-81\cdot[27+(-77)]$
$=-81\cdot(27-77)$
$=-81\cdot(-50)$
$=81\cdot50$
$=4050$
2) $(-16)\cdot32-(-4)^2\cdot18$
$=(-16)\cdot32-16\cdot18$
$=-16\cdot(32+18)$
$=-16\cdot50$
$=-800$
3) $(-2)^4\cdot289-16\cdot189$
$=16\cdot289+16\cdot(-189)$
$=16\cdot[289+(-189)]$
$=16\cdot(289-189)$
$=16\cdot100$
$=1600$
4) $41\cdot(-18)+41\cdot(-81)-41$
$=1\cdot(-18)+41\cdot(-81)+41\cdot(-1)$
$=41\cdot[(-18)+(-81)+(-1)]$
$=41\cdot(-18-81-1)$
$=41\cdot(-99-1)$
$=41\cdot(-100)$
$=-4100$
5) $17\cdot(-37)-23\cdot37-46\cdot(-37)$
$=17\cdot(-37)+23\cdot(-37)-46\cdot(-37)$
$=-37\cdot(17+23-46)$
$=-37\cdot(40-46)$
$=-37\cdot(-6)$
$=37\cdot6$
$=222$
6) $-48+48\cdot(-78)+48\cdot(-21)$
$=48\cdot(-1)+48\cdot(-78)+48\cdot(-21)$
$=48\cdot[(-1)+(-78)+(-21)]$
$=48\cdot(-1-78-21)$
$=48\cdot(-79-21)$
$=48\cdot(-100)$
$=-4800$
7) $29\cdot(-13)+27\cdot(-29)+(-14)\cdot(-29)$
$=-29\cdot13+27\cdot(-29)+(-14)\cdot(-29)$
$=-29\cdot[13+27+(-14)]$
$=-29\cdot(40-14)$
$=-29\cdot26$
$=-754$
$\text{#}Toru$
a) 23 + 25 + 27 + 29 + 31 + 33 + 35
= 23 + ( 25 + 35 ) + ( 27 + 33 ) + ( 29 + 31 )
= 23 + 60 + 60 + 60
= 23 + 60 x 3
= 23 + 180
= 203
b) 4 . 36 . 25 . 50
= 4 . 4 .9 . 25 . 25 . 2
= 4 . 25 . 4 . 25 . 9 . 2
= 100 . 100 . 9 . 2
= 10 000 . 18
= 180 000
c) 32 . 125 . 3
= 4 . 8 . 5 . 25 . 3
= 4 . 25 . 8 . 5 . 3
= 100 . 8 . 5 . 3
= 800 . 5 . 3
= 4000 . 3
= 12000
d, 36 . 19 + 36 . 81
= 36 . ( 19 + 81 )
= 36 . 100
= 3600
e, 78 . 31 + 78 . 24 + 78 . 17 + 22 x 72
= 78 . ( 31 + 24 + 17 ) + 22 x 72
= 78 . 72 + 22 . 72
= 72 . ( 78 + 22 )
= 72 . 100
= 7200
A)23+25+27+29+31+33+35
= (33+27)+(25+35)+(29+31)+23
=60+60+60+23
=60x3+23
=180+23
=203
B)4.36.25.50=(36.25).(4.50)
=(4.9.25).(2.2.50)
=(4.25).9 .(2.50).2
=100.9.100.2
=100.(9+2)
=100 .11
=1100
C)32.125.3=(4.8).125.3
=(125.8).(4.3)
=1000.12
=12000
D)36.19.36.81=36.(19+81)
= 36.100
=3600
E)78.31.+78.24+78.17+22x72=78.31+78.24+78.17+ (16+6).72
=78.31+78.24+78.17+78.16
=78.(31+24+17+16)
=78.88
=6864
a) `27 .75 + 25.27 -150`
`=27 xx (75 + 25)-150`
`=27 xx 100-150`
`=2700-150`
`=2550`
b) `142-[50-(2^3 .10-2^3 .5)]`
`=142-[50-2^3 .(10-5)]`
`=142-(50-8 .5)`
`=142-(50-40)`
`=142-10`
`=132`
c) `375:{32-[4+(5.3^2-42)]}-14`
`=375:{32-[4+(45-42)]}-14`
`=375:[32-(4+3)]-14`
`=375: 25 -14`
`=15-14`
`=1`
a. 27 . 75 + 25 . 27 - 150
= 27. (75 + 25) - 150
= 27 . 100 - 150
= 2700 - 150
= 2550
b. 142 - [50 - (23.10 - 23.5)]
= 142 - [50 - (8 . 10 - 8 . 5)]
= 142 - {50 - [8 . (10 - 5)]}
= 142 - (50 - 40)
= 142 - 10
= 132
c. 375 : {32 – [ 4 + (5. 32 – 42)]} – 14
= 375 : {32 – [ 4 + (5. 9 – 42)]} – 14
= 375 : {32 – [ 4 + (45 – 42)]} – 14
= 375 : {32 – [ 4 + 3]} – 14
= 375 : {32 –7} – 14
= 375 : 25 - 14
= 15 - 14
= 1
\(1.3^3+3^2-\left(2^7:2^5+7^8:7^7\right)\\ =27+9-\left(2^2+7\right)\\ =36-11\\ =25\)
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