a: \(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

=>\(2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

=>\(2A+A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}+...+2^2-2\)

=>\(3A=2^{101}-2\)

=>\(A=\dfrac{2^{101}-2}{3}\)

b: Sửa đề: \(A=\dfrac{2\cdot8^4\cdot27^2+4\cdot6^9}{2^7\cdot6^7+2^7\cdot40\cdot9^4}\)

\(A=\dfrac{2\cdot2^{12}\cdot3^6+2^2\cdot2^9\cdot3^9}{2^7\cdot2^7\cdot3^7+2^7\cdot2^3\cdot5\cdot3^8}\)

\(=\dfrac{2^{11}\cdot3^6\left(2^3+3^3\right)}{2^{10}\cdot3^7\left(2^4+5\cdot3\right)}\)

\(=\dfrac{2}{3}\cdot\dfrac{4+27}{16+15}=\dfrac{2}{3}\)

c: \(B=\dfrac{4^5\cdot9^4-2\cdot6^4}{2^{10}\cdot3^8+6^8\cdot20}\)

\(=\dfrac{2^{10}\cdot3^8-2\cdot2^4\cdot3^4}{2^{10}\cdot3^8+2^8\cdot2^2\cdot5\cdot3^8}\)

\(=\dfrac{2^5\cdot3^4\left(2^5\cdot3^4-1\right)}{2^{10}\cdot3^8\left(1+5\right)}=\dfrac{1}{2^5\cdot3^4}\cdot\dfrac{32\cdot81-1}{6}\)

\(=\dfrac{2591}{2^6\cdot3^5}\)

help

b: \(\dfrac{4^5\cdot9^4-2\cdot6^9}{2^{10}\cdot3^8+6^8\cdot20}\)

\(=\dfrac{2^{10}\cdot3^8-2^{10}\cdot3^9}{2^{10}\cdot3^8+3^8\cdot2^{10}\cdot5}\)

\(=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^{11}\cdot3^9}\)

\(=\dfrac{1}{2}\cdot\dfrac{-2}{3}=\dfrac{-1}{3}\)

Sửa đề câu a) phải là (-2020/2021)⁰

Xin lỗi mn

\(a,=\dfrac{3}{4}+\dfrac{15}{6}\cdot\dfrac{1}{5}-\dfrac{1}{36}\cdot9-\dfrac{2020}{2021}=\dfrac{3}{4}+\dfrac{1}{2}-\dfrac{1}{4}-\dfrac{2020}{2021}=1-\dfrac{2020}{2021}=\dfrac{1}{2021}\\ b,=\dfrac{2^{10}\cdot3^8-2\cdot2^9\cdot3^9}{2^{10}\cdot3^8+2^8\cdot3^8\cdot2\cdot5}=\dfrac{2^{10}\cdot3^8\left(1-3\right)}{2^9\cdot3^8\left(2+5\right)}=\dfrac{2\left(-2\right)}{3}=-\dfrac{4}{3}\)

300

300

= 300 

Biểu thức =\(\frac{15}{34}+\frac{4}{27}+\frac{19}{34}+\frac{23}{27}\)  ( rút gọn đó )

              =\(\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{4}{27}+\frac{23}{27}\right)\)

              =\(\frac{15+19}{34}+\frac{4+23}{27}\)= \(\frac{34}{34}+\frac{27}{27}\)

              = \(1+1=2\)

Oke nhá !!

=2.Hết gấp nha

bang 2

15/34 + 4/27 + 38/68 + 69/81

= (15/34 + 4/27) + ( 38/68 + 69/81)

=   541/918       +     1295/918

=               2

số dài quá tui rút gọn nha:2,1

\(\frac{15}{34}+\frac{4}{27}+\frac{38}{68}+\frac{69}{81}=\frac{15}{34}+\frac{4}{27}+\frac{19}{34}+\frac{23}{27}\)

\(=\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{4}{27}+\frac{23}{27}\right)\)

\(=\frac{34}{34}+\frac{27}{27}=1+1=2\)

Bằng 2 bạn nhé

Mình chắc 100%

Ủng hộ vì mình là người đầu tiên

=30/68+12/81+38/68+69/81

=1+1

=2

Ai tích mình mình tích lại cho

bằng 2 đó bạn

9+167/216

= 9.773148148

tớ viết là hỗn số nha