Bài 1:

Ta có:

\(\left(\frac{1}{10}\right)^{15}=\left(\frac{1}{5}\right)^{3.5}=\left(\frac{1}{125}\right)^5\)

\(\left(\frac{3}{10}\right)^{20}=\left(\frac{3}{10}\right)^{4.5}=\left(\frac{81}{10000}\right)^5\)

Lại có:

\(\frac{1}{125}=\frac{80}{10000}< \frac{81}{10000}\Rightarrow\left(\frac{1}{125}\right)^5< \left(\frac{81}{10000}\right)^5\)

\(\Rightarrow\left(\frac{1}{10}\right)^{15}< \left(\frac{3}{10}\right)^{20}\)

Bài 2:

Ta có:

\(A=\frac{13^{15}+1}{13^{16}+1}\Rightarrow13A=\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)

\(B=\frac{13^{16}+1}{13^{17}+1}\Rightarrow13B=\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)

Mà \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\)

\(\Rightarrow1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\)

\(\Rightarrow13A>13B\Rightarrow A>B\)

a) \(\frac{3^{15}.19+3^{15}.13}{3^{13}.16}\) =\(\frac{3^{15}.\left(19+13\right)}{3^{13}16}\) =\(\frac{3^{15}.32}{3^{13}.16}=\frac{3^{13}.3^2.32}{3^{13}.16}=\frac{3^2.2^4.2}{2^4}=18\)

Phần b bạn tự tách ra rồi nhóm lần lượt là ra mik chỉ làm phần a thôi nha

k cho mik nha

\(B=\frac{(3\cdot4\cdot2^{16})}{11\cdot2^{13}\cdot4^{11}-16^9}\)

\(=\frac{(2^2)^2\cdot(2^{16})^2\cdot3^2}{2^{13}\cdot(2^2)^{11}\cdot11-(2^4)^9}\)

\(=\frac{2^4\cdot2^{32}\cdot3^2}{2^{13}\cdot2^{22}\cdot11-2^{36}}\)

\(=\frac{2^{36}\cdot3^2}{2^{35}\cdot11-2^{36}}\)

\(=\frac{2^{36}\cdot3^2}{2^{35}\cdot(11-2)}\)

\(=\frac{2^1\cdot3^2}{9}\)

\(=\frac{2\cdot3^2}{3^2}=2\)

\(=\dfrac{3^2\cdot2^{36}}{11\cdot2^{13}\cdot2^{22}-2^{36}}=\dfrac{3^2\cdot2^{36}}{2^{35}\cdot9}=2\)

Ta có : 

\(13A=\frac{13^{16}+13}{13^{16}+1}=\frac{13^{16}+1+12}{13^{16}+1}=\frac{13^{16}+1}{13^{16}+1}+\frac{12}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)

\(13B=\frac{13^{17}+13}{13^{17}+1}=\frac{13^{17}+1+12}{13^{17}+1}=\frac{13^{17}+1}{13^{17}+1}+\frac{12}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)

Vì \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\) nên \(1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\) hay \(13A>13B\)

\(\Rightarrow\)\(A>B\)

Vậy \(A>B\)

Chúc bạn học tốt ~ 

Phùng Minh Quân ơi tớ cảm ơn nhưng tớ tính máy tính ra A = B ạ ( ko có ý gì đâu )

B > A

Mk nghĩ thế thui