\(\dfrac{4^9\cdot36+64^4}{100\cdot16^4}=\dfrac{2^{20}\cdot3^2+2^{24}}{2^{18}\cdot5^2}=\dfrac{2^{20}\left(3^2+2^4\right)}{2^{18}\cdot5^2}=4\)

 ko bt

Bài 1 :

a) 37581 - 9999 = 37581 - 10000 - 1 = 27581 - 1 = 27580

k cho mình nha bạn ! 

a)37581-9999=37581-(9999+1-1)=37581-(10000+1)=37581-10000-1=27581+1=27582

1/4 . 2/6 . 3/8 . ... .30/62 .31/64 = 2^x

(1/2 . 1/2).(2/3 . 1/2).(3/4 . 1/2). ... .(30/31 . 1/2).(31/32 . 1/2) = 2^x

(1/2.1/2. ... .1/2).(1/2 . 2/3 . 3/4. ... .30/31 . 31/32) = 2^x

   (31 số 1/2) 

(1/2)^31.  = 2^x

=> 0=x+36

      x=0-36

      x=-36

Vậy x=-36

Theo mk nghĩ,mk làm đúng nha .Tk cho mk

Để mk sửa phần này một chút

\((\frac{1}{2})^{31}\cdot\frac{1\cdot2\cdot3.....30\cdot31}{2\cdot3\cdot4.....31\cdot32}=2^x\)

\(\frac{1^{31}}{2^{31}}\cdot\frac{1}{32}=2^x\)

\(\frac{1}{2^{31}}\cdot\frac{1}{2^5}=2^x\)

\(\frac{1}{2^{36}}=2^x\)

\(1=2^x\cdot2^{36}\)

\(2^0=2^x+36\)

Rồi bn tự suy luận nha

\(\frac{1}{4}.\frac{2}{6}.\frac{3}{8}.........................\frac{31}{64}=\frac{1}{2^x}\)

Có 31 thừa số

\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}\right)...................\left(\frac{1}{2}.\frac{31}{32}\right)=\frac{1}{2^x}\)

\(\Leftrightarrow\left(\frac{1}{2}.\frac{1}{2}...............\frac{1}{2}\right).\left(\frac{1}{2}.\frac{2}{3}...............\frac{31}{32}\right)=\frac{1}{2^x}\)

Có 31 thừa số                                            Có 31 thừa số

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1.2....................31}{2.3..............32}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{32}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{31}}.\frac{1}{2^5}=\frac{1}{2^x}\)

\(\Leftrightarrow\frac{1}{2^{36}}=\frac{1}{2^x}\)

\(\Leftrightarrow x=36\)

Vậy x=36

Chúc bạn học tốt

a, 100 + 98 + 96 + ... + 2 - 9 7 - 95 - .. -1

=  100 + (98 - 97) + (96-95) + ... +  + ... + (2 - 1)

= 100 + 1 + 1 + 1 +.. +1

= 100 + 1 x49

= 100 + 49 

= 149

b , 1 + 2 - 3 - 4 + 5 + 6 - .... -299 - 330 +301 + 302 

 =( 1 + 2 - 3) + ( -4 + 5 + 6 -7 )  +... +(298 - 299 -300 +301 ) + 302

= 0 + 0 + .. + 0 + 302

= 302 

c)  2 . 31 . 12 + 4 . 6 . 42 + 8 . 27 . 3

=24.31+24.42+24.27

=24.(31+42+27)

=24.100

=2400

d)

=36x(28+82)+64x(69+41)

=36x110+64x110

=110x(26+64)

=110x100

=11000

d) dãy tính trên có số số tự nhiên là: (99-1):2+1=50(số)

99-97+95-93+91-89+...+7-5+3-1(50:2=25 cặp)

(99-97)+(95-93)+(91-89)+...+(7-5)+(3-1) (25 cặp)

2+2+2+2+2+...+2+2(25 số 2)

2x25=50

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + \(\dfrac{8}{1}\)

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

=  1 + 1 + 8

=  2 + 8

= 10

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{10}{20}\)

=  \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (\(\dfrac{2}{2}\) + \(\dfrac{3}{3}\) + \(\dfrac{4}{4}\) + \(\dfrac{5}{5}\)+ \(\dfrac{6}{6}+\dfrac{7}{7}+\dfrac{8}{8}\) + \(\dfrac{10}{10}\))

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x (1 + 1 +1 + 1+ 1+ 1+ 1 +1)

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) x 1 x 8

= \(\dfrac{1}{2}\) + \(\)\(\dfrac{1}{2}\) x 8

= \(\dfrac{1}{2}\) + 4

= \(\dfrac{9}{2}\) 

c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)

= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

=  \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)

= \(\dfrac{10+10+10+10+5}{10}\)

= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)

= \(\dfrac{10\times4+5}{10}\)

= \(\dfrac{45}{10}\)

= \(\dfrac{9}{2}\)

a; \(\dfrac{1}{4}\) + \(\dfrac{2}{5}\) + \(\dfrac{6}{8}\) + \(\dfrac{9}{15}\) + \(\dfrac{8}{1}\)

  = (\(\dfrac{1}{4}\) + \(\dfrac{6}{8}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{9}{15}\)) + 8

= (\(\dfrac{1}{4}\) + \(\dfrac{3}{4}\)) + (\(\dfrac{2}{5}\) + \(\dfrac{3}{5}\)) + 8

= 1 + 1 + 8

= 2 + 8

= 10

b; \(\dfrac{1}{2}\) + \(\dfrac{2}{4}\) + \(\dfrac{3}{6}\) + \(\dfrac{4}{8}\) + \(\dfrac{5}{10}\) + \(\dfrac{6}{12}\) + \(\dfrac{7}{14}\) + \(\dfrac{8}{16}\) + \(\dfrac{9}{18}\) + \(\dfrac{10}{20}\)

= \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\) + \(\dfrac{1}{2}\)

= \(\dfrac{1}{2}\) x 10

= 5

c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)

= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

=  \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)

= \(\dfrac{10+10+10+10+5}{10}\)

= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)

= \(\dfrac{10\times4+5}{10}\)

= \(\dfrac{45}{10}\)

= \(\dfrac{9}{2}\)

1/5+4/10+9/15+25/25+36/30+49/35+64/40+81/45

=1/5 + (4/10:2) +  (9/15:3)+25/25  +  (36/30:6)+  (49/35:7) +  (64/40:8)  +  (81/45:9)

=1/5 + 1/5 + 1/5 + 1 + 1/5 + 1/5 + 1/5 + 1/5

=1/5 x 7 + 1

=12/5