Bài 3 : Rút gọn
a) 273 - 184 / 316 - 24
b) 219 . 273 + 15 . 49 . 94 / 69 . 210 + 1210
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Lời giải:
\(P=\frac{2^{19}.27^3+15.4^9.9^4}{6^9.2^{10}+12^{10}}\\ =\frac{2^{19}.3^9+3.5.2^{18}.3^8}{2^9.3^9.2^{10}+2^{20}.3^{10}}\\ =\frac{2^{19}.3^9+2^{18}.3^9.5}{2^{19}.3^9+2^{20}.3^{10}}\\ =\frac{2^{18}.3^9(2+5)}{2^{19}3^9(1+2.3)}\\ =\frac{1}{2}\)
Rút gọn biểu thức
\(\text{a,x+(-30)-[95+(-40)+(-30)]}\)
\(=x+\left(-30\right)-95+40+30\)
\(=x-95+40=x-55\)
\(\text{a+(273-120)-(270-120)}\)
\(=a+273-120-270+120\)
\(=a+273-270=a+3\)
\(\text{b-(294+130)+(94+130)}\)
\(=b-294-130+94+130\)
\(=b-294+94=b-200\)
a) x + (- 30) - [95 + (- 40) + 5 + (- 30)]
= x + (-60) = x - 60
b) a + ( 273 - 120 ) - ( 270 - 120 )
= a + 3
c) b - ( 294 + 130 ) + ( 94 + 130 )
= b - 648
cho tổng S=5+8+11+14+...
a,tìm số hạng thứ 100 của tổng
b,tính tổng 100 số hạng đầu tiên
a) x + ( - 30 ) - [ 95 + ( - 40) + 5 + ( - 30) ]
= x - 30 - 95 + 40 - 5 + 30
= x -60
b) a + ( 273 - 120 ) - ( 270 - 120 )
= a + 273 -120 -270 + 120
= a+ 3
c) b - ( 294 + 130 ) + ( 94 + 130 )
= b - 294 -130 +94 +130
= b - 200
a: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)
=>\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)
=>\(2A+A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+...+2^2-2\)
=>\(3A=2^{101}-2\)
=>\(A=\dfrac{2^{101}-2}{3}\)
b: Sửa đề: \(A=\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)
\(A=\dfrac{2\cdot2^{12}\cdot3^6+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)
\(=\dfrac{2^{11}\cdot3^6\left(2^3+3^3\right)}{2^{10}\cdot3^7\left(2^4+5\cdot3\right)}\)
\(=\dfrac{2}{3}\cdot\dfrac{4+27}{16+15}=\dfrac{2}{3}\)
c: \(B=\dfrac{4^5\cdot9^4-2\cdot6^4}{2^{10}\cdot3^8+6^8\cdot20}\)
\(=\dfrac{2^{10}\cdot3^8-2\cdot2^4\cdot3^4}{2^{10}\cdot3^8+2^8\cdot2^2\cdot5\cdot3^8}\)
\(=\dfrac{2^5\cdot3^4\left(2^5\cdot3^4-1\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{1}{2^5\cdot3^4}\cdot\dfrac{32\cdot81-1}{6}\)
\(=\dfrac{2591}{2^6\cdot3^5}\)
a) x+(-30)-(95-40-30+x)
=x+(-30)-95+40+30-x
=(x-x) +[(-30)-95+40+30]
=-55
b) a+(273-a-120)-(270-120)
=a+273-a-120-150
=(a-a)+(273-120-150)
=3
c)b-(294+130)+(94+130)
=b-424+224
=b-(424-224)
=b-200
a. -30x-(95-40-30)
-30x-95+40+30
-30x-25
(rut gon: -5(6x-5)
Nhung y sau tuong tu nhe ban
rút gọn dễ :))
\(a,-a-\left(b-a-c\right)\)
\(=-a-b+a+c\)
\(=-b+c\)
\(b,-\left(a-c\right)-\left(a-b+c\right)\)
\(=-a+c-a+b-c\)
\(=-2a+b\)
\(c,-\left(a-b+c\right)-\left(a+b+c\right)\)
\(=-a+b-c-a-b-c\)
\(=-2a-2c\)
\(\text{a, x + (-30) - [95 + (-40) + (-30)]}\)
\(x+\left(-30\right)-95+40+30\)
\(=x-95+40\)
\(=x-55\)
b, a + (273 - 120) - (270 - 120)
\(=a+273-120-270+120\)
\(=a+\left(273-270\right)+\left(-120+120\right)\)
\(=a+3\)
c, b - (294 + 130) + (94 + 130)
\(=b-294-130+94+130\)
\(=b+\left(-294+94\right)+\left(-130+130\right)\)
\(=b-200\)
2. Đơn giản biểu thức sau khi bỏ ngoặc:
a, -a - (b - a - c)
\(=-a-b+a+c\)
\(=\left(-a+a\right)-b+c\)
\(=-b+c\)
b, -(a - c ) - (a - b + c)
\(=-a+c-a+b-c\)
\(=\left(-a-a\right)+\left(c-c\right)+b\)
\(=-2a+b\)
c, -( a - b + c) - (a + b + c)
\(=-a+b-c-a-b-c\)
\(=\left(-a-a\right)+\left(b-b\right)+\left(-c-c\right)\)
\(-2a+-2c\)
học tốt !!