làm bừa thui,ai tích mình mình tích lại

Số số hạng là : 

Có số cặp là :

50 : 2 = 25 ( cặp )

Mỗi cặp có giá trị là :

99 - 97 = 2 

Tổng dãy trên là :

25 x 2 = 50

Đáp số : 50

\(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}.\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}.\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)

Bn vào phần Câu hỏi tương tự ý. Có 1 bn cũng có câu hỏi giống như thế.

-Học tốt-

mọi người giúp mình nha

a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.5^8}=7\)

b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^9.5^2.5^3}{3.5.5^4.3^8}=\frac{3^9.5^5}{3^9.5^5}=1\)

c) \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)

d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2\)

\(=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2\)

\(=\frac{1}{100}+\frac{121}{100}=\frac{122}{100}=\frac{61}{50}\)

a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=\frac{7^3.5^8}{7^2.5^8}=7\)

b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3^9.5^2.5^3}{5.3.5^4.3^8}=\frac{3^9.5^5}{5^5.3^9}=1\)

c) \(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{91}.3^{16}}=\frac{2^{50}.3^{16}\left(3^{45}+2^{40}\right)}{2^{51}.3^{16}\left(3^{45}+2^{40}\right)}=\frac{1}{2}\)

d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(-\frac{1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{122}{100}=1,22\)

\(=\frac{\left(2^{31}.3^{16}\right).2^{19}.3^{45}+\left(2^{31}.3^{16}\right).2^{59}}{\left(2^{31}.3^{16}\right).2^{20}.3^{45}+\left(2^{31}.3^{16}\right)}\\ =\frac{\left(2^{31}.3^{16}\right).\left(2^{19}.3^{45}+2^{59}\right)}{\left(2^{31}.3^{16}\right).\left(2^{20}.3^{45}+1\right)}\\ =\frac{2^{19}.3^{45}+2^{59}}{2^{20}.3^{45}+1}\)

\(2^{19}.\frac{3^{45}+2^{40}}{2^{20}.3^{45}+1}\)

\(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{31}.3^{16}}=\frac{2^{50}.3^{16}+3^{45}+2^{50}+2^{40}.3^{16}}{2^{31}+3^{20}+2^{31}.3^{16}}\)

                                 \(=556758,4881\)

=\(\frac{2^{50}.+2^{90}}{2^{51}+2^{31}}=\frac{2^{19}}{2^{39}}=\frac{1}{1048576}\)

K nha

a) \(\frac{7^3.5^8}{49.25^4}=\frac{7^3.5^8}{7^2.\left(5^2\right)^4}=7.\frac{5^8}{5^8}=7\)

b) \(\frac{3^9.25.5^3}{15.625.3^8}=\frac{3.3^8.5^2.5^3}{3.5.5^4.3^8}=\frac{5^5}{5^5}=1\)

c) Đề hơi sai roi bạn oi

d) \(\left(\frac{2}{5}-\frac{1}{2}\right)^2+\left(\frac{1}{2}+\frac{3}{5}\right)^2=\left(\frac{-1}{10}\right)^2+\left(\frac{11}{10}\right)^2=\frac{1}{100}+\frac{121}{100}=\frac{61}{50}\)

Khanh Nguyễn Ngọc  :câu d ko sai bạn nha dấu "/" là trên nhó

\(\frac{2^{50}.3^{61}+2^{90}.3^{16}}{2^{51}.3^{61}+2^{31}.3^{61}}\)

\(=\frac{3^{61}\left(2^{50}+2^{90}\right)}{3^{61}\left(2^{51}+2^{31}\right)}\)

\(=\frac{2^{50}+2^{90}}{2^{51}+2^{31}}\)

\(=\frac{2^{31}\left(2^{19}+2^{59}\right)}{2^{31}\left(1+2^{20}\right)}\)

\(=\frac{2^{19}+2^{59}}{1+2^{20}}\)

= ???????? 

:3

khoo qua minh chiu 

k dong vien minh di ban 

( noi nho ) : tk nay khon vai 

so sánh 

ta có 

333⁴⁴⁴=333^4.111=(333⁴)¹¹¹

444³³³=444^3.111=(444³)¹¹¹

So sánh 333⁴và 444³ ta có 

333⁴=(3.111)⁴=3⁴ . 111⁴=81.111⁴

444³=(4.111)³=4³. 111³=64. 111³

Vì 81.111⁴>64.111³

Suy ra 333⁴⁴⁴>444³³³

\(B=\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+\frac{7}{\left(3.4\right)^2}+....+\frac{61}{\left(30.31\right)^2}\)

\(=\frac{3}{1^2.2^2}+\frac{5}{2^2.3^2}+\frac{7}{3^2.4^2}+...+\frac{61}{30^2.31^2}\)

\(=\frac{2^2-1^2}{1^2.2^2}+\frac{3^2-2^2}{2^2.3^2}+\frac{4^2-3^2}{3^2.4^2}+...+\frac{31^2-30^2}{30^2.31^2}\)

\(=\frac{1}{1^2}-\frac{1}{2^2}+\frac{1}{2^2}-\frac{1}{3^2}+....+\frac{1}{30^2}-\frac{1}{30^2}\)

\(=1-\frac{1}{31^2}=1-\frac{1}{961}=\frac{960}{961}\)

P/s: Bài này chỉ tính được giá trị "gần đúng" của biểu thức thôi nhé!

\(\frac{21}{54}+\frac{3}{75}:\frac{\left(\frac{39}{65}+0,415-\frac{33}{600}\right)\frac{21}{91}}{7^2-18,25+13\frac{15}{36}-16\frac{17}{102}}\)

\(\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{\left(0,6+0,415-0,055\right)0,23}{49-18,25+\frac{483}{36}-\frac{1649}{102}}\)

\(\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{\left(0,6+0,415-0,055\right)0,23}{49-18,25+13,41-16,1}\)

\(\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{0,96.0,23}{28,06}\Leftrightarrow\frac{21}{54}+\frac{3}{75}:\frac{0,2208}{28,06}\)

\(\Leftrightarrow\frac{21}{54}+\left(\frac{3}{75}:\frac{0,2208}{28,06}\right)\Leftrightarrow\frac{21}{54}+\left(\frac{3}{75}.\frac{28,06}{0,2208}\right)=\frac{21}{54}+\frac{61}{12}=\frac{197}{36}\)

P/s: Giải bài này mà mệt cả đầu =((