m = 19.3.30 và n = 31.2.30

=> m= 57.30 và n = 62.30

Vì 57<62 => m<n

a)

+) m = 19. 90 = 19. (3. 30) = (19. 3). 30

+) n = 31. 60 = 31. (3. 20) = (20. 3). 31

Vì 19 < 20; 30 < 31 nên (19. 3). 30 < (20. 3). 31 hay m < n.

Vậy m < n.

b) p = 2 011. 2 019 = 2 011. (2 015 + 4) = 2 011. 2 015 + 2 011. 4 

    q = 2 015. 2 015 = (2 011 + 4). 2 015 = 2 011. 2 015 + 4. 2015

       = 2 011. 2 015 + 2 015. 4

Vì 2 011 < 2 015 nên 2 011. 4 < 2 015. 4 

hay 2 011. 2 015 + 2 011. 4 < 2 011. 2 015 + 2 015. 4

Do đó p < q

Vậy p < q.

\(A=\frac{100^{2014}+2}{3}-\frac{100^{2015}+17}{9}\)

Quy đồng mẫu, ta được:

 \(A=\frac{3\left(100^{2014}+2\right)}{3\cdot3}-\frac{100^{2015}+17}{9}\)

=> \(A=\frac{3\left(100^{2014}+2\right)}{9}-\frac{100^{2015}+17}{9}=\frac{3\left(100^{2014}+2\right)-\left(100^{2015}+17\right)}{9}\)

=> \(B=-9A=\)\(-9\cdot\frac{3\left(100^{2014}+2\right)-\left(100^{2015}+17\right)}{9}=-\left\{\left[3\left(100^{2014}+2\right)-\left(100^{2015}+17\right)\right]\right\}\)

MK BIẾT TỚI ĐÂY THÔI

k nha b = 18

A=-1/2*-2/3*-3/4*..*-2013/2014

A=-1*-2*-3*...*-2013/2*3*4*...*2014

A=-1/2014

ta có(-1)^2015=-1

B=-1/2015>-1/2014=A

nên A<B

a: \(6\sqrt{3}=\sqrt{108}>\sqrt{54}=3\sqrt{6}\)

\(\Rightarrow5^{6\sqrt{3}}>5^{3\sqrt{6}}\)

b: \(\sqrt{2}\cdot2^{\dfrac{2}{3}}=2^{\dfrac{1}{2}}\cdot2^{\dfrac{2}{3}}=2^{\dfrac{1}{2}+\dfrac{2}{3}}=2^{\dfrac{7}{6}}\)

\(\left(\dfrac{1}{2}\right)^{-\dfrac{4}{3}}=2^{\left(-1\right)\cdot\left(-\dfrac{4}{3}\right)}=2^{\dfrac{4}{3}}\)

mà \(\dfrac{7}{6}< \dfrac{8}{6}=\dfrac{4}{3}\).

nên \(\sqrt{2}\cdot2^{\dfrac{2}{3}}< \left(\dfrac{1}{2}\right)^{-\dfrac{4}{3}}\).

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: \(120>-546\)

\(\Rightarrow B>A\)

=8.5*0.01+7.5*0.01+2.5*0.01+1.5*0.01

=(8.5+7.5+2.5+1.5)*0.01

=20*0.01

ta co h cua 2 so la;ta lay [0,085+0,015]+[0,075+0,025]=0,1+0,1=0,2