Đặt \(A=2^{49}+2^{48}+\cdots+2^2+2\)

=>\(2A=2^{50}+2^{49}+\cdots+2^3+2^2\)

=>2A-A=\(2^{50}+2^{49}+\cdots+2^3+2^2-2^{49}-2^{48}-\cdots-2^2-2\)

=>\(A=2^{50}-2\)

Ta có: \(2^{50}-2^{49}-2^{48}-\cdots-2^2-2\)

\(=2^{50}-\left(2^{50}-2\right)\)

\(=2^{50}-2^{50}+2=2\)

Đặt N=2^49+2^48+...+2^3+2^2+2

=>2N=2^50+2^49+...+2^4+2^3+2^2

=>2N-N=2^50-2

=>N=2^50-2

=>M=2^50-2^50+2=2

\(27\cdot36+73\cdot99+27\cdot14-49\cdot7\)

\(=27\cdot\left(36+14\right)+73\cdot99-49\cdot7\)

\(=27\cdot50+6884=1350+6884=8234\)

\(\dfrac{5^6}{5^4}+2^3\cdot2^2-1^{2017}\)

\(=5^2+2^5-1\)

=25+32-1

=25+31

=56

a:

Sửa đề: \(B=\frac{5^{99}+1}{5^{100}+1}\)

Ta có: \(5A=\frac{5^{50}+5}{5^{50}+1}=\frac{5^{50}+1+4}{5^{50}+1}=1+\frac{4}{5^{50}+1}\)

\(5B=\frac{5^{100}+5}{5^{100}+1}=\frac{5^{100}+1+4}{5^{100}+1}=1+\frac{4}{5^{100}+1}\)

Ta có: \(5^{50}+1<5^{100}+1\)

=>\(\frac{4}{5^{50}+1}>\frac{4}{5^{100}+1}\)

=>\(\frac{4}{5^{50}+1}+1>\frac{4}{5^{100}+1}+1\)

=>5A>5B

=>A>B

b: \(\frac{A}{3}=\frac{3^{49}-5}{3^{49}-15}=\frac{3^{49}-15+10}{3^{49}-15}=1+\frac{10}{3^{49}-15}\)

\(\frac{B}{3}=\frac{3^{50}-5}{3^{50}-15}=\frac{3^{50}-15+10}{3^{50}-15}=1+\frac{10}{3^{50}-15}\)

Ta có: \(3^{49}-15<3^{50}-15\)

=>\(\frac{10}{3^{49}-15}>\frac{10}{3^{50}-15}\)

=>\(\frac{10}{3^{49}-15}+1>\frac{10}{3^{50}-15}+1\)

=>\(\frac{A}{3}>\frac{B}{3}\)

=>A>B

a) 25^2:5^2 = 25 

nếu đề là 25^3:5^2 thì :

=(5^2)^3:5^2

=5^6:5^2

=5^4

b) =(3/7)^21:[(3/7)^2] ^6

=(3/7)^21:[(3/7)^2]

=(3/7)^21-12

^{=3/7^9}

3-(-6/7)^0+(1/2)^2:2

lẹ giúp mk nhé

\(Tacó\frac{8^{19}\times14^{11}}{49^6\times2^{68}}\)

\(=\frac{\left(2^3\right)^{19}\times2^{11}\times7^{11}}{\left(7^2\right)^6\times2^{68}}\)

\(=\frac{2^{57}\times2^{11}\times7^{11}}{7^{12}\times2^{68}}\)

\(=\frac{2^{68}\times7^{11}}{7^{12}\times2^{68}}\)

\(=\frac{1\times1}{7\times1}\)

\(=\frac{1}{7}\)

a) x²-24x​-25=x²+x-25x-25

=x(x+1)-25(x+1)

=(x-25)(x+1)

b) x²-y²+14x​+49=(^​x²​+14x+49)-y²

=(x+7)²​-y²​=(x-y+7)(x+y+7)

\(2^{98}\) và \(9^{49}\)

Ta có: \(2^{98}=\left(2^2\right)^{49}=4^{49}\)

Vì \(4^{49}< 9^{49}\) nên \(2^{98}< 9^{49}\)

ttttttttttthhhhhhhhhhaaaaaaaaaaaannnnnnnnnnnkkkkkkkkkkkk

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