a) Ta có: \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)

Mà \(\frac{1}{32}=\left(\frac{1}{2}\right)^5\)

\(\Rightarrow\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\Rightarrow m=5\)

b)Ta có:  \(\frac{343}{125}=\left(\frac{7}{5}\right)^3\)

Mà \(\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\Rightarrow n=3\)

\(a)\) \(\left(\frac{1}{2}\right)^m=\frac{1}{32}\)

\(\Leftrightarrow\)\(\left(\frac{1}{2}\right)^m=\frac{1^5}{2^5}\)

\(\Leftrightarrow\)\(\left(\frac{1}{2}\right)^m=\left(\frac{1}{2}\right)^5\)

\(\Leftrightarrow\)\(m=5\)

Vậy \(m=5\)

\(b)\) \(\frac{343}{125}=\left(\frac{7}{5}\right)^n\)

\(\Leftrightarrow\)\(\frac{7^3}{5^3}=\left(\frac{7}{5}\right)^n\)

\(\Leftrightarrow\)\(\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\)

\(\Leftrightarrow\)\(n=3\)

Vậy \(n=3\)

Chúc bạn học tốt ~ 

a, \(\frac{1}{2^m}=\frac{1}{32}\)

\(\Rightarrow\frac{1}{2^m}=\frac{1}{2^5}\)

\(\Rightarrow m=5\)

\(b,\frac{343}{125}=\left(\frac{7}{5}\right)^n\)

\(\Rightarrow\left(\frac{7}{5}\right)^3=\left(\frac{7}{5}\right)^n\)

\(\Rightarrow n=3\)

Ta có : \(\frac{2^7.3^4}{3^3.2^5}=\frac{2^2.3}{1.1}=4.3=12\)

k cho mk nha!

Ta lập biểu thức:

\(\frac{\left(2^7.3^4\right)}{3^3.2^5}=\frac{128.81}{27.32}=\frac{10368}{864}=12\)

Vì khi ta lập biểu thức ra và tính nó sẽ được vậy chứ khong có lí do nha bạn ~~

\(=\frac{2^7\cdot3^4}{3^3\cdot2^5}=\frac{2^2\cdot3}{1\cdot1}=12\)

2: \(\left(\dfrac{1}{6}\right)^{10}=\dfrac{1}{6^{10}}\)

(1/2)^50=1/2^50

mà 6^10<2^50

nên (1/6)^10<(1/2)^50

3: 30^-50=1/30^50=(1/3)^500=(1/243)^100

5^-30=1/5^30=(1/125)^100

=>30^50<5^-30

Bài 6 :

a) \(\dfrac{625}{5^n}=5\Rightarrow\dfrac{5^4}{5^n}=5\Rightarrow5^{4-n}=5^1\Rightarrow4-n=1\Rightarrow n=3\)

b) \(\dfrac{\left(-3\right)^n}{27}=-9\Rightarrow\dfrac{\left(-3\right)^n}{\left(-3\right)^3}=\left(-3\right)^2\Rightarrow\left(-3\right)^{n-3}=\left(-3\right)^2\Rightarrow n-3=2\Rightarrow n=5\)

c) \(3^n.2^n=36\Rightarrow\left(2.3\right)^n=6^2\Rightarrow\left(6\right)^n=6^2\Rightarrow n=6\)

d) \(25^{2n}:5^n=125^2\Rightarrow\left(5^2\right)^{2n}:5^n=\left(5^3\right)^2\Rightarrow5^{4n}:5^n=5^6\Rightarrow\Rightarrow5^{3n}=5^6\Rightarrow3n=6\Rightarrow n=3\)

Bài 7 :

a) \(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Rightarrow3^x\left(1+3^2\right)=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Rightarrow10.3^x=3^{34}+3^{36}\)

\(\Rightarrow10.3^x=3^{34}\left(1+3^2\right)=10.3^{34}\)

\(\Rightarrow3^x=3^{34}\Rightarrow x=34\)

b) \(5^{x+1}-5^x=100.25^{29}\Rightarrow5^x\left(5-1\right)=4.5^2.\left(5^2\right)^{29}\)

\(\Rightarrow4.5^x=4.25^{2.29+2}=4.5^{60}\)

\(\Rightarrow5^x=5^{60}\Rightarrow x=60\)

c) Bài C bạn xem lại đề

d) \(\dfrac{3}{2.4^x}+\dfrac{5}{3.4^{x+2}}=\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{10}}\)

\(\Rightarrow\dfrac{3}{2.4^x}-\dfrac{3}{2.4^8}+\dfrac{5}{3.4^{x+2}}-\dfrac{5}{3.4^{10}}=0\)

\(\Rightarrow\dfrac{3}{2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)+\dfrac{5}{3.4^2}\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)=0\)

\(\Rightarrow\left(\dfrac{1}{4^x}-\dfrac{1}{4^8}\right)\left(\dfrac{3}{2}+\dfrac{5}{3.4^2}\right)=0\)

\(\Rightarrow\dfrac{1}{4^x}-\dfrac{1}{4^8}=0\)

\(\Rightarrow\dfrac{4^8-4^x}{4^{x+8}}=0\Rightarrow4^8-4^x=0\left(4^{x+8}>0\right)\Rightarrow4^x=4^8\Rightarrow x=8\)

5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha5 ha 4 dm² = 5,000004 ha

\(\left(\frac{1}{2}\right)^{40}=\left(\frac{1}{2}\right)^{10\cdot4}=\left(\frac{1}{16}\right)^{10}\)

Mà ta có

\(\left(\frac{1}{32}\right)^{10}< \left(\frac{1}{16}\right)^{10}\)

\(\Rightarrow\left(\frac{1}{2}\right)^{40}>\left(\frac{1}{32}\right)^{10}\)

(1/5)mũ 2 .n=(1/5)mũ 15

=>n=(1/5)mũ 13

(\(\frac{1}{5}\))² .n = (\(\frac{1}{125}\))³ - n

<=> \(\frac{1}{25}\)n +n = \(\frac{1}{5^9}\)

<=> \(\frac{26}{25}\)n = \(\frac{1}{5^9}\)

<=> n = \(\frac{1}{5^9}\): \(\frac{26}{25}\)= \(\frac{1}{2031250}\)

1.a)A = (1 - 1/3)(1-2/5)...(1-5/5)....(1-9/5)

      =(1-1/3)....0.....(1-9/5)

      =0

     =>đpcm.

b)ta xét:

1/2² = 1/2x2 < 1/1x2

.............

1/8² = 1/8x8 <1/7x8

=>B < 1/1x2 + 1/2x3 ... + 1 + 1/7x8

<=> B <1 - 1/2 + 1/2  - 1/3  + ... + 1/7 - 1/8

<=> B < 1 - 1/8 = 7/8 < 1

=> B < 1 => đpcm

2.a) Đặt m = 2007(2006+2007) = 2006(2006 + 2007) + (2006+2007)

      Đặt n = 2006(2007+2008) = 2006(2006+2007) + (2006 + 2006)

Ta thấy : (2006+2007) > (2006 + 2006) => m > n , áp dụng công thức "a.d > c.d <=> a/b > b/d (a,c thuộc Z// b,d thuộc N)

=> A > B

   b)ta có: D = 196 + 197/197 + 198 = (196/197+198) + (197/197+198) < 196/197 + 197/198 = C

=> C > D

c)gọi 20¹⁰ là a

ta thấy : (a + 1)(a-3) = (a - 1)(a - 3) + 2(a - 3) < (a - 1)(a - 3) + 2(a - 1) = (a - 1)(a - 1)

áp dụng: ad > bc <=> a/b > c/d ( a,b,c,d thuộc Z// b,d > 0)

=> E > F