Ta thấy : 2\(^2\)=4=4.1\(^2\)

  4\(^2\)=16=4.2\(^2\)

   6\(^2\)=36=4.3\(^2\)

     ...

  20\(^2\)=400=4.10\(^2\)

 =>S=2\(^2\)+4\(^2\)+6\(^2\)+...+20\(^2\)=4.(1\(^2\)+2\(^2\)+3\(^2\)+...+10\(^2\))

 = 4.385 

 =1540

  Vậy tổng S = 1540

1155 nhé bn nhưng mk k bt cách làm

Bn nào bt giúp mk vs

\(A=\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\)

\(A=\left(12^2-1^2\right)+\left(14^2-3^2\right)+\left(16^2-5^2\right)+\left(18^2-7^2\right)+\left(20^2-9^2\right)\)\(A=\left(12+1\right)\left(12-1\right)+\left(14+3\right)\left(14-3\right)+\left(16-5\right)\left(16+5\right)+\left(18-7\right)\left(18+7\right)+\left(20-9\right)\left(20+9\right)\)

\(A=11.13+11.17+11.21+11.25+11.29\)

\(A=11.\left(13+17+21+25+29\right)\)

\(A=11.\left[\left(13+17\right)+\left(21+29\right)+25\right]\)

\(A=11.\left(30+50+25\right)\)

\(A=11.105=1155\)

Ta thấy A gấp 1²+2²+....+10² 4 lần nên Tổng A gấp 4 lần nó

=> A=385.4=1540

\(\left(12^2+14^2+16^2+18^2+20^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\\\Rightarrow\left[\left(2^2.6^2\right)+\left(2^2.7^2\right)....+\left(2^2.10^2\right)\right]-\left(1^2+3^2+...+9^2\right)\\ \Rightarrow2^2.\left(6^2+7^2....+.10^2\right)-\left(1^2+3^2+5^2+7^2+9^2\right)\\ \Rightarrow4.330-165=1155\)

Câu 1 :

a) \(4.\left(\frac{1}{32}\right)^{-2}:\left(2^3.\frac{1}{16}\right)\)

\(=2^2.32^2:\left(\frac{1}{8}.16\right)=\left(2.32\right)^2:2=64^2:2\)

\(=2048=2^{11}\)

b) \(5^2.3^5.\left(\frac{3}{5}\right)^2\)

\(=\left(5.\frac{3}{5}\right)^2.3^5=3^2.3^5=3^7\)

VIẾT CÁC BIỂU THỨC DƯỚI DẠNG LUỸ THỪA CỦA 1 SỐ HỮU TỈ

\(a,4\cdot\left(\frac{1}{32}\right)^{-2}:\left(2^3\cdot\frac{1}{16}\right)\\ =4\cdot1024:\left(8\cdot\frac{1}{16}\right)\\ =4\cdot1024:\frac{1}{2}\\ =2\cdot1024\\ =2\cdot2^{10}\\ =2^{11}\)

\(b,5^2\cdot3^5\cdot\left(\frac{3}{5}\right)^2\\ =5^2\cdot\left(\frac{3}{5}\right)^2\cdot3^5\\ =3^2\cdot3^5\\ =3^7\)

2 SO SÁNH

\(a,10^{20}\text{ và }9^{10}\)

Có: \(9^{10}=\left(3^2\right)^{10}=3^{20}\)

\(\Rightarrow10^{20}>3^{20}\\ \text{hay}\text{ }10^{20}>9^{10}\)

\(b,\left(-5\right)^3\text{ và }\left(-3\right)^{50}\)

Có: \(\left(-3\right)^{50}=3^{50}\)

\(\Rightarrow\left(-5\right)^3< 3^{50}\\ \text{hay }\left(-5\right)^3< \left(-3\right)^{50}\)

\(c,64^3\text{ và }16^{12}\)

Có: \(64^3=\left(4^3\right)^3=4^9;16^{12}=\left(4^2\right)^{12}=4^{24}\)

\(\Rightarrow4^9< 4^{24}\\ hay\text{ }64^3< 16^{12}\)

\(d,\left(\frac{1}{16}\right)^{10}\text{ và }\left(\frac{1}{2}\right)^{50}\)

Có: \(\left(\frac{1}{2}\right)^{50}=\left(\frac{1}{2}\right)^{5\cdot10}=\left[\left(\frac{1}{2}\right)^5\right]^{10}=\left(\frac{1}{32}\right)^{10}\)

\(\Rightarrow\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{32}\right)^{10}\\ \text{hay }\left(\frac{1}{16}\right)^{10}>\left(\frac{1}{2}\right)^{50}\)