A. 7,9

B. 36,57

C. 52,047

D. 306,009

\(5^{x-2}-3^2=2^4-\left(2^8\cdot2^4-2^{10}\cdot2^2\right)\)

\(\Rightarrow5^{x-2}-3^2=2^4-\left(2^{12}-2^{12}\right)\)

\(\Rightarrow5^{x-2}-9=16-0\)

\(\Rightarrow5^{x-2}=16+9\)

\(\Rightarrow5^{x-2}=25\)

\(\Rightarrow5^{x-2}=5^2\)

\(\Rightarrow x-2=2\)

\(\Rightarrow x=2+2\)

\(\Rightarrow x=4\)

Vậy: x=4

Ta có:

\(15\cdot31\cdot37+110\cdot102\)

\(=5\cdot3\cdot31\cdot37+5\cdot22\cdot102\)

\(=5\cdot\left(3\cdot31\cdot37+22\cdot102\right)\)

Nên sẽ chia hết cho 5 nên tổng đó là hỗn số

\(\left(1-\dfrac{1}{1+2}\right)\cdot\left(1-\dfrac{1}{1+2+3}\right)\cdot\left(\dfrac{1}{1+2+3+...+2006}\right)\)

\(=\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{6}\right)\cdot\left\{\dfrac{1}{\left(2006+1\right)\left[\left(2006-1\right):1+1\right]}\right\}\)

\(=\dfrac{2}{3}\cdot\dfrac{5}{6}\cdot\dfrac{1}{2007\cdot2006}\)

\(=\dfrac{10}{18}\cdot\dfrac{1}{4026042}\)

\(=\dfrac{5}{9}\cdot\dfrac{1}{4026042}\)

\(=\dfrac{5}{36234378}\)

\(1\dfrac{3}{5}=1+\dfrac{3}{5}=1+0,6=1,6\)

Chọn C

Ta thấy dãy số C

5,1 > 5,01 > 4,03 > 2,9 

Chọn C

Chữ số 4 trong số 189,234 là: \(0,004=\dfrac{4}{1000}\)

Chọn A

\(-a^2\) và \(\left(-a^2\right)\) không có gì khác nhau cả 

Khác nhau khi:

\(-a^2\) và \(\left(-a\right)^2\)

Bởi vì:

\(-a^2=-a^2\)

\(\left(-a\right)^2=a^2\)

\(2+4+8+16+32+64+128+256\)

\(=\left(128+2\right)+\left(256+4\right)+\left(64+16\right)+\left(32+8\right)\)

\(=130+260+80+40\)

\(=390+120\)

\(=610\)