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

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

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

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

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

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

a) \(5^n.25=125^2\)

\(\Rightarrow5^n.5^2=\left(5^3\right)^2\)

\(\Rightarrow5^n.5^2=5^6\)

\(\Rightarrow5^n=5^6:5^2\)

\(\Rightarrow5^n=5^4\)

\(\Rightarrow n=4\)

Vậy \(n=4.\)

b) \(3^n.9^2=27^3\)

\(\Rightarrow3^n.\left(3^2\right)^2=\left(3^3\right)^3\)

\(\Rightarrow3^n.3^4=3^9\)

\(\Rightarrow3^n=3^9:3^4\)

\(\Rightarrow3^n=3^5\)

\(\Rightarrow n=5\)

Vậy \(n=5.\)

c) \(2^4.4^n=8^6\)

\(\Rightarrow\left(2^2\right)^2.4^n=2^{18}\)

\(\Rightarrow4^2.4^n=\left(2^2\right)^9\)

\(\Rightarrow4^2.4^n=4^9\)

\(\Rightarrow4^n=4^9:4^2\)

\(\Rightarrow4^n=4^7\)

\(\Rightarrow n=7\)

Vậy \(n=7.\)

Chúc bạn học tốt!

Cảm ơn bn nhiều lắm !

Bài làm:

Bài 1

a) \(\left(x-\frac{1}{2}\right)^2=0\) 

 \(\rightarrow\left(x-\frac{1}{2}\right)^2=0^2\)

 \(\rightarrow x-\frac{1}{2}=0\) 

 \(\Rightarrow x=\frac{1}{2}\)

Bài 2

a) \(25^3\div5^2=\left(5^2\right)^3\div5^2=5^6\div5^2=5^4\)

b) \(\left(\frac{3}{7}\right)^{21}\div\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}\div\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{21}\div\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)

c) \(3-\left(\frac{-6}{7}\right)^0+\left(\frac{1}{2}\right)^2\div2=3-1+\frac{1}{4}\times\frac{1}{2}=2+\frac{1}{8}=\frac{17}{8}\)

Bài 3

a) \(9\times3^3\times\frac{1}{81}\times3^2=3^2\times3^3\times\frac{1}{3^4}\times3^2=3^3\)

b) \(4\times2^5\div\left(2^3\times\frac{1}{16}\right)=2^2\times2^5\div\left(2^3\times\frac{1}{2^4}\right)=2^7\div\frac{1}{2}=2^6\)

c) \(3^2\times2^5\times\left(\frac{2}{3}\right)^2=3^2\times2^5\times\frac{2^2}{3^2}=3^2\times\frac{2^7}{3^2}=2^7\)

d) \(\left(\frac{1}{3}\right)^2\times\frac{1}{3}\times9^2=\left(\frac{1}{3}\right)^3\times3^4=\frac{1}{3^3}\times3^4=3^1\)

Các bạn giải từng bước ra cho mình nhé, cảm ơn các bạn

Theo đề : Ta có : 1 .2 + 2.3 + 3.1 + a . 6 + 5.3 + 6.1 +7.4 + 8.2 + 9.1 +10 .2 / 25 = 5,16 
=>   1 .2 + 2.3 + 3.1 + a . 6 + 5.3 + 6.1 +7.4 + 8.2 + 9.1 +10 .2 = 5,16 . 25 
=>  1 .2 + 2.3 + 3.1 + a . 6 + 5.3 + 6.1 +7.4 + 8.2 + 9.1 +10 .2  =  129
=>  a.6 + (1 .2 + 2.3 + 3.1 + 5.3 + 6.1 +7.4 + 8.2 + 9.1 +10 .2)  = 129 
=> a .6  +   105 = 129
=> a .6              = 129 - 105
=> a .6              =  24
=> a                  = 24 : 6 
=> a                  = 4 
Vậy a = 4

1:a:4827;6915

b:5670

2:825

b:9180;21780

bài 1: a) 4827 ; 6915 .b) 5670

bài 2:a) 825.b) 9180;21780

đây có phải toàn 7 k vậy lớp 6 bọn mik đã học rồi 

không trả lời thì thôi đừng có nói nhiều