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a) \(-215+\left(-427\right)-\left(-515\right)-573\)
\(=-215+\left(-427\right)+515-573\)
\(=\left(-215+515\right)+\left(-427-573\right)\)
\(=-300+-1000=-1300\)
b) \(-68+68.\left(-76\right)+68.\left(-23\right)\)
\(=68.\left(-1\right)+68.\left(-76\right)+68.\left(-23\right)\)
\(=68.\left(-1+-76+-23\right)\)
\(=68.-10=-6800\)
4:
a: \(\dfrac{\left(158-x\right)}{7}=20\)
=>\(158-x=7\cdot20=140\)
=>x=158-140=18
b: \(2x-138=23\cdot32\)
=>\(2x-138=736\)
=>2x=736+138=874
=>x=437
c: \(231-\left(x-6\right)=\dfrac{1339}{13}\)
=>\(231-\left(x-6\right)=103\)
=>x-6=128
=>x=128+6=134
d: \(10+2x=\dfrac{45}{43}\)
=>\(2x=\dfrac{45}{43}-10=-\dfrac{385}{43}\)
=>\(x=-\dfrac{385}{43}:2=-\dfrac{385}{86}\)
e: \(70-5\left(2x-3\right)=45\)
=>\(5\left(2x-3\right)=70-45=25\)
=>2x-3=5
=>2x=8
=>x=4
g: \(156-\left(x+61\right)=82\)
=>x+61=156-82=74
=>x=74-61=13
a ) 2 15 b ) − 2 5 c ) 1 d ) 1 e ) − 5 3 f ) 0 g ) 2 3 5 h ) 1
a) \(9^3\cdot3^2\)
\(=\left(3^2\right)^3\cdot3^2\)
\(=3^6\cdot3^2\)
\(=3^8\)
b) \(x^7\cdot x:x^4\)
\(=x^8:x^4\)
\(=x^4\)
c) \(7\cdot3^9+3^{10}+51\cdot3^8\)
\(=3^8\cdot\left(7\cdot3+3^2+51\right)\)
\(=3^8\cdot81\)
\(=3^8\cdot3^4\)
\(=3^{12}\)
d) \(5^{15}\cdot125^3\cdot625\)
\(=5^{15}\cdot5^9\cdot5^4\)
\(=5^{28}\)
a) 1 − 5 + 9 − 5 = 1 + 9 − 5 = 10 − 5 = − 2
b) 5 15 + − 8 24 = 1 3 + − 1 3 = 1 + − 1 3 = 0
515+[72+(-515)+(-32)]
=[515+(-515)]+[72+(-32)]
=0+40
=40
\(515.\left(2-128.128\right).\left(-515\right)\)
\(=515.\left(2-16384\right).\left(-515\right)\)
\(=515.\left(-16382\right).\left(-515\right)\)
\(=\left(-8436730\right).\left(-515\right)\)
\(=4344915950\)
Đề như thế này chắc đúng hơn nhỉ?
\(\frac{5.14^{15}.9^9-4.3^{20}.8^9}{5.2^9.6^{19}-7.2^{29}.27^6}\)
Đặt \(A=5.14^{15}.9^9-4.3^{20}.8^9\) và \(B=5.2^9.6^{19}-7.2^{29}.27^6\), ta được:
\(\text{+)}\) \(A=5.14^{15}.9^9-4.3^{20}.8^9=5.\left(2^2\right)^{15}.\left(3^2\right)^9-2^2.3^{20}.\left(2^3\right)^9=5.2^{30}.3^{18}-2^2.3^{20}.2^{27}\)
\(A=5.2^{30}.3^{18}-2^{29}.3^{20}=2^{29}.3^{18}\left(5.2-3^2\right)=2^{29}.3^{18}\)
\(\text{+)}\) \(B=5.2^9.6^{19}-7.2^{29}.27^6=5.2^9.\left(2.3\right)^{19}-7.2^{29}.\left(3^3\right)^6=5.2^9.2^{19}.3^{19}-7.2^{29}.3^{18}\)
\(B=5.2^{28}.3^{19}-7.2^{29}.3^{18}=2^{28}.3^{18}\left(5.3-7.2\right)=2^{28}.3^{18}\)
Do đó, \(\frac{A}{B}=\frac{2^{29}.3^{18}}{2^{28}.3^{18}}=2\)
5^20:(5^15.6 + 5^15.9)
= 5^20 : (5^15(6+9))
= 5^20: 5^15.5.3
= 5^4.3
= 625 . 3
=1875