Nhớ trình Bày cách Làm nha

a) 2^27=(2^3)^9=8^9

    3^18=(3^2)^9=9^9

    Vì 8^9 bé hơn 9^9 nên 2^27 bé hơn 3^18

a: 27^4=(3^3)^4=3^12<3^18

b: 49^4=(7^2)^4=7^8

c: 9^16=(9^2)^8=81^8>27^8

bằng 28 bn nhé

Ta có: \(a=27^5=\left(3^3\right)^5=3^{15}\)

           \(b=\frac{3^{16}+3^{17}}{4}=\frac{3^{16}\left(1+3\right)}{4}=3^{16}\)

Vậy \(a< b\)

Câu 1:

\(A=27^2.32^3=\left(3^3\right)^2.\left(2^5\right)^3=3^6.2^{15}\)

\(B=6^{16}=2^{16}.3^{16}\)

Từ \(\hept{\begin{cases}2^{15}< 2^{16}\\3^6< 3^{16}\end{cases}\Leftrightarrow2^{15}.3^6< 2^{16}.3^{16}\Leftrightarrow}A< B\)

Câu 2:

\(A=1+2+2^2+2^3+...+2^{2016}\)

<=>\(2A=2\left(1+2+2^2+2^3+...+2^{2016}\right)\)

<=>\(2A=2+2^2+2^3+2^4...+2^{2017}\)

<=>\(2A-A=\left(2+2^2+2^3+2^4+...+2^{2017}\right)-\left(1+2+2^2+2^3+...+2^{2016}\right)\)

<=>\(A=2^{2017}-1< 2^{2017}=B\)

Vậy A<B

muốn viết dấu mũ như thế kia thì viết thế nào hả bạn ?

A = 27² . 32³                            B = 6¹⁶

A = ( 3³ )² . ( 2⁵ )³                        B = ( 2 .3 )¹⁶

A = 3⁶ . 2¹⁵                               B = 2¹⁶ . 3¹⁶

      ta thấy 3⁶ < 3¹⁶ ; 2¹⁵ < 2¹⁶

\(\Rightarrow A< B\)

chúc bạn học giỏi ^^

:37 + ( - 27 ) và ( - 27 )  + 37 = 0

16 + ( - 16 ) và ( - 105 ) + 105 = 0 

hai số đối nhau có tổng bằng 0 

Ta có: A = \(\frac{-2}{11}+\frac{6}{7}+\frac{1}{2}+\frac{-9}{11}+\frac{1}{7}\)
A = \(\left(\frac{-2}{11}+\frac{-9}{11}\right)+\left(\frac{6}{7}+\frac{1}{7}\right)+\frac{1}{2}\)

A = \(-1+1+\frac{1}{2}\)

A = \(\frac{1}{2}\)

B = \(\left(\frac{9}{16}+\frac{8}{27}\right)+\left(1+\frac{7}{16}+\frac{-19}{27}\right)\)

B = \(\frac{9}{16}+\frac{8}{27}+1+\frac{7}{16}-\frac{19}{27}\)

B = \(\left(\frac{9}{16}+\frac{7}{16}\right)+1+\left(\frac{8}{27}-\frac{19}{27}\right)\)

B = \(1+1-\frac{11}{27}\)

B = \(\frac{43}{27}\)

Mà 1/2 < 43/27 (Vì 1/2 < 1; 43/27 > 1)

=> A < B

                       Giải

\(A=\frac{-2}{11}+\frac{6}{7}+\frac{1}{2}+\frac{-9}{11}+\frac{1}{7}\)

\(\Leftrightarrow A=\left(\frac{-2}{11}+\frac{-9}{11}\right)+\left(\frac{6}{7}+\frac{1}{7}\right)+\frac{1}{2}\)

\(\Leftrightarrow A=\frac{-11}{11}+\frac{7}{7}+\frac{1}{2}\)

\(\Leftrightarrow A=-1+1+\frac{1}{2}\)

\(\Leftrightarrow A=\frac{1}{2}< 1\left(1\right)\)

\(B=\left(\frac{9}{16}+\frac{8}{27}\right)+\left(1+\frac{7}{16}+\frac{-19}{27}\right)\)

\(\Leftrightarrow B=\left(\frac{9}{16}+\frac{7}{16}\right)+\left(\frac{8}{27}+\frac{-19}{27}\right)+1\)

\(\Leftrightarrow B=\frac{16}{16}+\frac{-11}{27}+1\)

\(\Leftrightarrow B=1+\frac{-11}{27}+1\)

\(\Leftrightarrow B=2+\frac{-11}{27}\)

\(\Leftrightarrow B=\frac{43}{27}\)\(>1\left(2\right)\)

Từ (1) và (2) suy ra A < B