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Bài 1 :
a) \(...=45\left(56+44\right)-500=45.100-500=4500-500=4000\)
b) \(...=3^2.6-6^{18}+1=45+1-6^{18}=46-6^{18}\)
c) \(...=756\left(66+48-14\right)=756.100=75600\)
d) \(...=8.15-\left(149-7^2\right)=120-\left(149-49\right)=120-100=20\)
Bài 2 :
a) \(x-21=46\Rightarrow x=21+46\Rightarrow x=87\)
b) \(2^x.4=128\Rightarrow2^x=32\Rightarrow2^x=2^5\Rightarrow x=5\)
c) \(3x+27=162\Rightarrow3x=162-27\Rightarrow3x=135\Rightarrow x=45\)
d) \(4x-8=4^{2023}.4^{2021}\)
\(\Rightarrow4x-8=4^{2023+2021}\)
\(\Rightarrow4x-8=4^{4044}\)
\(\Rightarrow4x=4^{4044}+8\)
\(\Rightarrow x=\left(4^{4044}+8\right):4\)
\(\Rightarrow x=4^{4043}+2\)
Lời giải:
Gọi biểu thức là $A$
\(A=\frac{2^{10}.3^8+5.(2^2)^5.3^8}{2^{10}.(3^3)^3-2^{10}.(3^2)^4}=\frac{2^{10}.3^8+5.2^{10}.3^8}{2^{10}.3^9-2^{10}.3^{8}}\)
\(=\frac{2^{10}.3^8(1+5)}{2^{10}.3^8(3-1)}=\frac{6}{2}=3\)
\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)
\(=\frac{3^{10}+\left(3 \cdot2\right)^2}{5\cdot3^8+5\cdot4}\)
\(=\frac{3^{10}+3^2\cdot2^2}{5\cdot\left(3^8+4\right)}\)
\(=\frac{3^2\cdot\left(3^8+2^2\right)}{5\cdot\left(3^8+4\right)}\)
\(=\frac{3^2\cdot\left(3^8+4\right)}{5\cdot\left(3^8+4\right)}\)
\(=\frac{3^2}{5}\)
\(=\frac{9}{5}\)
{ x2 - [ 62 - ( 82 -9.7 )3 -7.5 ]3 -5.3 }3 =1 ... {x2 - [62 - 13 -7.5]3 - 5.3}3=1. {x2 - [36 - 1 -7.5]3 - 5.3}3=1. {x2 - [36 - 1 - 35]3 - 5.3}3=1. {x2 - [35 - 35]3 -5.3}3=1. {x2 - 03 - 5.3}3=1. {x2 - 0 -5.3}3=1. {x2 - 0 - 15}3=1. {x.x - 0 - 15}3=1. {x.x + 0+15}3=1. {x.x +15}3=1.
\(1.\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=3^2=9\)
\(2.\dfrac{8^5.3^{15}}{2^{14}.81^4}=\dfrac{2^{15}.3^{15}}{2^{14}.3^{16}}=\dfrac{2}{3}\)
Ý 1:
\(\dfrac{27^4.4^3}{9^5.8^2}=\dfrac{\left(3^3\right)^4.\left(2^2\right)^3}{\left(3^2\right)^5.\left(2^3\right)^2}=\dfrac{3^{12}.2^6}{3^{10}.2^6}=3^2=9\)
Ý 2:
\(\dfrac{8^5.3^{15}}{2^{14}.81^4}=\dfrac{\left(2^3\right)^5.3^{15}}{2^{14}.\left(3^4\right)^4}=\dfrac{2^{15}.3^{15}}{2^{14}.3^{16}}=\dfrac{2^{14}.2.3^{15}}{2^{14}.3^{15}.3}=\dfrac{2}{3}\)
\(\frac{3^{10}+6^2}{5.3^8+20}=\frac{3^2+6^2}{5+20}=\frac{9^2}{25}=\frac{81}{25}=\frac{9}{5}\)
\(\frac{3^{10}+6^2}{5\cdot3^8+20}\)
\(=\frac{3^{10}+\left(3\cdot2\right)^2}{5\left(3^8+4\right)}\)
\(=\frac{3^{10}+3^2\cdot2^2}{5\left(3^8+4\right)}\)
\(=\frac{3^2\left(3^8+4\right)}{5\left(3^8+4\right)}\)
\(=\frac{9}{5}\)
500 : [ 149 - ( 82 - 5 . 3 ) ]
= 500 : [ 149 - ( 64 - 15 ) ]
= 500 : [ 149 - 49 ]
= 500 : 100
= 5
_HT_