\(a,\dfrac{3^{43}+3^4}{3^{39}+1}\)

\(=\dfrac{3^4\cdot\left(3^{39}+1\right)}{3^{39}+1}\)

\(=3^4\)

\(=81\)

\(b,\dfrac{3^{10}.11+3^{10}.5}{3^9.2^4}\)

\(=\dfrac{3^{10}\left(11+5\right)}{3^9.2^4}\)

\(=\dfrac{3^{10}.16}{3^9.2^4}\)

\(=\dfrac{3^{10}.2^4}{3^9.2^4}=3\)

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 câu a :   a/3+b/2 > a+b/3+2

câu b:     lấy vd a=1 b=3 thì sẽ =1/3 +3/2 và 1 +3 /3+2  khi quy đồng lên thì 1/3 +3/2=55/30 còn 1+3/3+2 =24/30

 55/30>24/30 suy ra :a/3+b/2> a+b/3+2

câu c:     9/3+8/2=7        9+8/3+2=17/5

  C=5.4+8.4-2

 D=5+8-4-2 từ đó suy ra C>D

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C > D VÌ : 5x4 > 5; 8x4 > 8-4;-2=-2

10³⁰=10.10.10.10.........10=300

còn 2¹⁰⁰⁰=2.2.2.2.2.2............2-2000

 vậy biểu thức B lớn hơn

Ta có :

A = \(10^{30}=\left(10^3\right)^{10}=100^{10}\)

B = \(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

=> A < B

bài ni cũng dễ mà các bạn fhân tích số mũ ra là ok

210 . 13 + 210 . 6528 .104

= 210 . ( 13 + 6528 ) . 104

= 210 . 6541 .104

= 142855440

B=C*[13*37*(5*3-15)]=0

\(A=\dfrac{2^{10}\cdot78}{2^8\cdot26\cdot4}=\dfrac{78}{26}=3\)

Đặt \(A=\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}\)

\(A>\frac{3}{14}+\frac{3}{14}+\frac{3}{14}+\frac{3}{14}+\frac{3}{14}=\frac{3}{14}.5=\frac{15}{14}>1\)

\(A< \frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}=\frac{3}{10}.5=\frac{15}{10}=\frac{3}{2}< 2\)

Vậy \(1< A< 2\)

=>\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}>\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}\)

mà \(\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}+\frac{3}{15}=\frac{15}{15}=1\)

=>\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}>1\)(1)

mà \(\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}+\frac{3}{10}=\frac{15}{10}< \frac{20}{10}=2\)

=>\(\frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< 2\)(2)

Từ (1) và (2) => \(1< \frac{3}{10}+\frac{3}{11}+\frac{3}{12}+\frac{3}{13}+\frac{3}{14}< 2\)