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a: A=3^2(1^2+2^2+...+10^2)
=9*385
=3465
b: B=2^3(1^3+2^3+...+10^3)
=8*3025
=24200
![](https://rs.olm.vn/images/avt/0.png?1311)
A = \(2^2.\left(1^2+2^2+3^2+...+10^2\right)=4.385=1540\)
B=\(3^2.\left(1^2+2^2+3^2+...+10^2\right)=385.9=3465\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=2^2+4^2+........+20^2\)
\(B=1^2.2^2+2^2.2^2+3^2.2^2+.......+10^2.2^2\)
\(B=2^2.\left(1^2+2^2+3^2+.......+10^2\right)\)
\(B=4.385\) (đề bài cho)
\(B=1540\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có :
\(S=\left(0,25\right)^2+\left(0,5\right)^2+...+\left(2,5\right)^2\)
\(\Rightarrow4S=2^2.\left(0,25\right)^2+2^2.\left(0,5\right)^2+.....+2^2.\left(2,5\right)^2\)
\(\Rightarrow4S=1^2+2^2+....+10^2\)
\(\Rightarrow4S=385\)
\(\Rightarrow S=\frac{385}{4}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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1.
a. \(\frac{5^4.18^4}{125.9^5.16}=\frac{5^4.2^4.3^8}{5^3.3^{10}.2^4}=\frac{5}{3^2}=\frac{5}{9}\)
2.
a . x : ( 0,25 ) 4 = ( 0,5 ) 2
=> x : ( 0,5 ) 8 = ( 0,5 ) 2
=> x = ( 0,5 ) 2 . ( 0,5 ) 8
=> x = ( 0,5 ) 10
=> x = \(\frac{1}{1024}\)
Bài 1.\(\frac{5^4\cdot18^4}{125\cdot9^5\cdot16}=\frac{5^4\cdot9^4\cdot2^4}{5^3\cdot9^5\cdot2^4}=\frac{5}{9}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x:\left(0,25\right)^4=\left(0,5\right)^2\)
\(x:\left(\frac{1}{4}\right)^4=\left(\frac{1}{2}\right)^2\)
\(x:\left[\left(\frac{1}{2}\right)^2\right]^4=\left(\frac{1}{2}\right)^2\)
\(x:\left(\frac{1}{2}\right)^8=\left(\frac{1}{2}\right)^2\)
\(x=\left(\frac{1}{2}\right)^2\cdot\left(\frac{1}{2}\right)^8=\left(\frac{1}{2}\right)^{10}=\frac{1}{1024}\)
\(1^2:0,25^2=16;2^2:0,5^2=16;....;10^2:2,5^2=16\Rightarrow B=\frac{385}{16}\)