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208 - 84: 12= 208- 7= 201
5^6 : 5^3 + 2^3.2^2= 5^3 + 2^5= 125 + 32= 1577
15 . 2^3 + 4 . 3^2 - 5.7= 15 . 8 + 4. 9 - 5.7= 120 + 36 - 35=156 - 35=121
164 . 53 + 47 . 164= 164.(53 + 47)=164. 100=16400
a) 11070 : {15 . [ 356 – ( 2110 – 2000 )]}
= 11070 : [15(356 – 110)] = 11070 : 3690 = 3
b) 62500 : { 50 2 : [ 112 – ( 52 – 2 3 . 5 )]}
= 62500 : { 2500 : [ 112 – ( 52 – 40 )]}
= 62500 : { 2500 : [ 112 – 12 ]}
= 62500 : { 2500 : 100 }
= 62500 : 25
= 2500
c) 3 3 . 5 3 – 20 . { 300 – [ 540 – 2 3 ( 7 8 : 7 6 + 7 0 )]}
= 3 3 . 5 3 – 20 . {300 – [ 540 – 2 3 (72 + 1 )]
= 3 3 . 5 3 – 20 . [ 300 – (540 - 8 . 50)
= 27 . 125 – 20 . [300 – ( 540 - 400 )]
= 3375 – 20 . ( 300 – 140 )
= 3375 – 20 . 160
= 3375 – 3200
= 175
\(\text{(−1)+(−3)+...+(−199)+(−201)(−1)+(−3)+...+(−199)+(−201)}\)
=\(\text{−(1+3+...+199+201)=−(1+3+...+199+201)}\)
=\(\dfrac{\left(201+1\right).\left[\left(201-1\right)\right]:2+1}{2}\)
= \(\dfrac{-200.102}{2}=\dfrac{-20400}{2}=-10200\)
\(\text{17 + ( − 20 ) + 23 + ( − 26 ) + . . . + 53 + ( − 56 ) = [ 17 + ( − 20 ) ] + [ 23 + ( − 26 ) ] + . . . + [ 53 + ( − 56 ) ] = ( − 3 ) + ( − 3 ) + . . . + ( − 3 ) = ( − 3 ) . ( 7 ) = − 21}\)
\(\text{=17 + ( − 20 ) + 23 + ( − 26 ) + . . . + 53 + ( − 56 ) = [ 17 + ( − 20 ) ] + [ 23 + ( − 26 ) ] + . . . + [ 53 + ( − 56 ) ] = ( − 3 ) + ( − 3 ) + . . . + ( − 3 ) = ( − 3 ) . ( 7 ) = − 21}\)
\(\text{ = ( − 3 ) + ( − 3 ) + . . . + ( − 3 )}\)
\(\text{= ( − 3 ) . ( 7 ) = − 21}\)
a)
204 - 84 : 12
= 204 - ( 84 : 12 )
= 204 - 7
= 107
b)
15 . 23 + 4 . 32 - 5 . 7
= 15 . 8 + 4 . 9 - 5 . 7
= 120 + 36 - 35
= 156 - 35
= 121
c)
56 : 53 + 23 . 22
= 5(6-3) + 2(3+2)
= 53 + 25
= 125 + 32
= 157
d) 164 . 53 + 47 . 164
= 164 . ( 53 + 47 )
= 164 . 100
= 16400
a,198
b,51
c,157
d,1640