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\(A=2^5.5^2-3^2-10\\ \\ A=32.25-9-10=800-9-10\\ \\ A=781\)
\(B=3^3.3^2+2^2+3^2\\ \\ B=3^{3+2}+4+9\\ \\ B=3^5+13=243+13\\ \\ B=256\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: =29-16-3*2=13-6=7
2: =35-12+(-14)-2
=23-16=7
3: =4*3125-32:16
=12500-2
=12498
4: =-452+67-75+452=-8
5: =18+99*18-3^5-2^5
=1800-275
=1525
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a) B = 3 3 . 3 2 + 2 2 + 3 2 = 256 = 16 2 .
b) D = 5 . 4 3 + 2 4 . 5 = 400 = 20 2
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b. (-274).71+(-274).29
= (-274).(71+29)
= (-274). 100
= -27400
(-274).71+(-274).29
=(-274).(71+29)
=(-274).100
=(-27400)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, A = 2 2 . 5 2 - 3 2 - 10 = 81 = 3 4 = 9 2
b, B = 3 3 . 3 2 + 2 2 + 3 2 = 256 = 16 2 = 2 8 = 4 4
c, C = 5 . 4 3 + 2 4 . 5 = 400 = 20 2
d, D = 5 3 + 6 3 + 7 3 + 79 . 2 2 = 1000 = 10 3
![](https://rs.olm.vn/images/avt/0.png?1311)
a) A = 2 5 . 5 2 - 3 2 - 10 = 81 = 3 4 ( = 9 2 ) .
b) B = 3 3 . 3 2 + 2 2 + 3 2 = 256 = 16 2 ( = 2 8 = 4 4 ) .
c) C = 5 . 4 3 + 2 4 . 5 = 400 = 20 2
d) D = 5 3 + 6 3 + 7 3 + 7 9 . 2 2 = 1000 = 10 3 .
![](https://rs.olm.vn/images/avt/0.png?1311)
a) Đặt: \(A=1+2^2+2^3+...+2^{10}\)
\(\Rightarrow2A=2\left(1+2^2+2^3+...+2^9+2^{10}\right)\)
\(\Rightarrow2A=2+2^3+2^4+...+2^{10}+2^{11}\)
\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{10}+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)
\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2-1\right)+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=0+0+...+1+\left(2^{11}-2^2\right)\)
\(\Rightarrow A=1+2^{11}-2^2=1+2048-4=2045\)
Vậy: \(1+2^2+2^3+...+2^{10}=2045\)
b)
a] \(60-3\left(x-1\right)=2^3\cdot3\)
\(\Rightarrow60-3\left(x-1\right)=24\)
\(\Rightarrow3\left(x-1\right)=36\)
\(\Rightarrow x-1=12\)
\(\Rightarrow x=13\)
b] \(\left(3x-2\right)^3=2\cdot2^5\)
\(\Rightarrow\left(3x-2\right)^3=2^6\)
\(\Rightarrow\left(3x-2\right)^3=\left(2^2\right)^3\)
\(\Rightarrow3x-2=2^2\)
\(\Rightarrow3x=6\)
\(x=2\)
c] \(5^{x+1}-5^x=500\)
\(\Rightarrow5^x\left(5-1\right)=500\)
\(\Rightarrow5^x\cdot4=500\)
\(\Rightarrow5^x=125\)
\(\Rightarrow5^x=5^3\)
\(\Rightarrow x=3\)
d] \(x^2=x^4\)
\(\Rightarrow x=x^2\)
\(\Rightarrow x-x^2=0\)
\(\Rightarrow x\left(1-x\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\1-x=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
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x + 20 + 21 + x + 22 + 23 + x + 24 + 25 + x + 26 + 27 + x + 28 + 29 + x + 30 = 330
6x + (30 + 20) . (30 - 20 + 1) : 2 = 330
6x + 50 . 11 : 2 = 330
6x + 275 = 330
6x = 330 - 275
6x = 55
x = 55 : 6
x = 55/6
\(x+20+21+x+22+23+x+24+25+x+26+27+x+28+29+x+30=330\)
\(\Rightarrow\left(x+x+x+x+x+x\right)+\left(20+21+22+23+24+25+26+27+28+29+30\right)=330\)
\(\Rightarrow6x+\left[\left(30-20\right):1+1\right]\left(20+30\right):2=330\)
\(\Rightarrow6x+11.50:2=330\)
\(\Rightarrow6x+275=330\)
\(\Rightarrow6x=55\)
\(\Rightarrow x=\dfrac{55}{6}\)
\(328-\left[x-\left(33.32-29:22\right).2\right]=274\)
\(328-\left[x-\left(1056-\frac{29}{22}\right).2\right]=274\)
\(x-2112+\frac{29}{11}=328-274\)
\(x-2112+\frac{29}{11}=54\)
\(x=54+2112-\frac{29}{11}\)
\(x=\frac{23797}{11}\)
vậy \(x=\frac{23797}{11}\)