+) 4M = \(\dfrac{4^{13}+4}{4^{13}+1}=1+\dfrac{3}{4^{13}+1}\)

+) 4N = \(\dfrac{4^{14}+4}{4^{14}+1}=1+\dfrac{3}{4^{14}+1}\)

Có 4¹³+1 < 4¹⁴+1

⇒ \(\dfrac{3}{4^{13}+1}\) > \(\dfrac{3}{4^{14}+1}\)

⇒ \(1+\dfrac{3}{4^{13}+1}\) > \(1+\dfrac{3}{4^{14}+1}\)

⇒ 4M > 4N

⇒ M > N

Nếu mà có sai sót gì thì cho mình xin lỗi nhé

a) Ta có: 

\(A=-3\cdot7\cdot\left(-2\right)\cdot\left(-13\right)\)

\(A=-21\cdot26\)

\(A=-546\)

\(B=-1\cdot\left(-2\right)\cdot\left(-3\right)\cdot\left(-4\right)\cdot5\)

\(B=2\cdot12\cdot5\)

\(B=2\cdot60\)

\(B=120\)

Mà: \(120>-546\)

\(\Rightarrow B>A\)

Bài 1: 

a: -8/12<0<-3/-4

b: -56/24<0<7/3

c: 4/25<1<15/13

=>-4/25>-15/13

Bài 2: 

a: =-60/45=-4/3

b: =4/15-3/2-8/5=8/30-45/30-48/30=-85/30=-17/6

1

Câu 4:

\(4^{n+2}-4^{n-1}=252\\ \Leftrightarrow4^{n-1}.\left(4^3-1\right)=252\\ \Leftrightarrow4^{n-1}.63=252\\ \Leftrightarrow4^{n-1}=\dfrac{252}{63}=4=4^1\\ \Rightarrow n-1=1\\ \Rightarrow n=2\)

Câu 7:

\(\left(\dfrac{36}{49}\right)^4:\left(-\dfrac{6}{7}\right)^6=\left(\dfrac{6}{7}\right)^{2.4}:\left(\dfrac{6}{7}\right)^6=\left(\dfrac{6}{7}\right)^8:\left(\dfrac{6}{7}\right)^6=\left(\dfrac{6}{7}\right)^{8-6}=\left(\dfrac{6}{7}\right)^2=\dfrac{36}{49}\)

Câu 8:

\(13^{96}=\left(13^3\right)^{32}=2197^{32}\\ 15^{64}=\left(15^2\right)^{32}=225^{32}\\ Vì:2197^{32}>225^{32}\left(Do:2197>225\right)\Rightarrow13^{96}>15^{64}\)