\(-382-\left[125+\left(-382\right)\right]-\left[\left(3210-697\right)+\left(-3210-957\right)\right]\)
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-385 -[1925 +(-382)]-[(3210-697)+(3210+597)]
= -385 -1925 +(-382)-[3210 -697-3210+597]
= -385 -1925 +(-382)- [3210-3210 +597-697]
= -385 + (-382) -1925 -[0+(-100)
= -385 +(-382)-1925-(-100)
=-767 -1925+100
= -2692 +100
= -2592
Ta có:-385-[ 1925+(-382) ] - [ ( 3210 - 697 )+(-3210+597) ]
=-385 - [ 1925-382 ] - [ 3210 - 697 - 3210+597 ]
=-385 - 1925 + 382 - [ ( 3210 - 3210 )+( 597 - 697 ) ]
= -3 - 1925 - [ 0 - 100 ]
= -1928 + 100 = -1828
a) \(A=\left(-1\right)^{2n}.\left(-1\right)^n.\left(-1\right)^{n+1}=\left(-1\right)^{3n+1}\)
b) \(B=\left(10000-1^2\right)\left(10000-2^2\right).........\left(10000-1000^2\right)\)
\(=\left(10000-1^2\right)\left(10000-2^2\right)......\left(10000-100^2\right)....\left(10000-1000^2\right)\)
\(=\left(10000-1^2\right)\left(10000-2^2\right).....\left(10000-10000\right).....\left(10000-1000^2\right)=0\)
c) \(C=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)..........\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right).....\left(\frac{1}{125}-\frac{1}{5^3}\right)......\left(\frac{1}{125}-\frac{1}{25^3}\right)\)
\(=\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)........\left(\frac{1}{125}-\frac{1}{125}\right).....\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
d) \(D=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-10^3\right)}\)
\(=1999^{\left(1000-1^3\right)\left(1000-2^3\right)........\left(1000-1000\right)}=1999^0=1\)
Sách Giáo Khoa
a) (-4).(+125).(-25).(-6).(-8) = [(-4).(-25)].[(+125).(-8)].(-6) = 100.(-1000).(-6) = 600000 b) (-98).(1 - 246) – 246.98 = -98 + 98.246 - 246.98 = -98 + 98.(246 - 246) = -98 + 98.0 = -98a) (-4).(+125).(-25).(-6).(-8)
= [(-4).(-25)].[(+125).(-8)].(-6)
= 100.(-1000).(-6)
= 600000
b) (-98).(1 - 246) – 246.98
= -98 + 98.246 - 246.98
= -98 + 98.(246 - 246)
= -98 + 98.0
= -98
a (-4) . (+3) . (-125) . (+25) . (-8)
=[(-4) . (+25)] . [(-125) . (-8)] . (+3)
=(-100) + (1000) . (+3)
= -300 000
b (-67) . (1 - 301) - 301 . 67
=(-67) . 1 + 67 . 301 - 67 . 301
= - 67
#)Giải :
a)\(2009^{\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-15^3\right)}=2009^{\left(1000-1^3\right)...\left(1000-10^3\right)...\left(1000-15^3\right)}=2009^0=1\)
b)\(\left(\frac{1}{125}-\frac{1}{1^3}\right)\left(\frac{1}{125}-\frac{1}{2^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...\left(\frac{1}{125}-\frac{1}{5^3}\right)...\left(\frac{1}{125}-\frac{1}{25^3}\right)=\left(\frac{1}{125}-\frac{1}{1^3}\right)...0...\left(\frac{1}{125}-\frac{1}{25^3}\right)=0\)
\(-382-\left[125+\left(-382\right)\right]-\left[\left(3210-697\right)+\left(-3210-957\right)\right]\)
\(=-382-125+382-3210+697+3210+957\)
\(=-125-697-957\)
\(=-1779\)
hok tốt!!