Bài 1: a) (2x+1)^{​2 ​}=​ 25

               (2x+1)^​2 = 5^​2

=> 2x + 1 = 5           hoặc      2x+1 = -5

=> x=2                   hoặc       x=-3

  b) 2^x+2 - 2^​x = 96

<=> 2^​x . 2^​2 - 2^​x = 96

<=> 2^​x(4-1) =96

<=>2^​x = 96 :3 = 32 = 2^​5 

<=> x = 5

c) (x-1)^​3 = 125

<=> (x-1)^​3 = 5^​3

<=> x-1=5

<=>x= 5 +1 = 6

Bài 2 :

a) Ta có :  7^​6+7^​5-7^​4 
              =7^​4(7^​2+7-1) 
              =7^​4.55=7^​4.5.11 chia hết cho 11 

b) Ta có:

81^​7-27^​9-9¹³
=(3^​4)^​7- (3^​3)^​9-^​   (3^​2)^​13 
=3²⁸ - 3²⁷- 3^​26
=3²⁶ (3^​2-3-1) 
 = 3²⁶.5 = 3^1​3.3^​2.5 = 45.3^1​3 chia hết cho 45

2 

a) (2x - 1)⁴ = 81

<=> \(\orbr{\begin{cases}2x-1=3\\2x-1=-3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x=4\\2x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=-1\end{cases}}}\)

a, \(\dfrac{4^2.4^3}{2^{10}}=\dfrac{4^5}{2^{10}}=\dfrac{\left(2^2\right)^5}{2^{10}}=\dfrac{2^{10}}{2^{10}}=1\)

b, \(\dfrac{2^7.9^3}{6^5.8^2}=\dfrac{2^7.\left(3^2\right)^3}{2^5.3^5.\left(2^3\right)^2}=\dfrac{2^7.3^6}{2^5.3^5.2^6}=\dfrac{3}{2^4}=\dfrac{3}{16}\)

c, \(\dfrac{9^7.5^6.125^9}{15^{15}.5^{18}}=\dfrac{3^{21}.5^6.5^{27}}{5^{15}.3^{15}.5^{18}}=\dfrac{3^{21}.5^{33}}{3^{15}.5^{33}}=3^6=729\)

d, \(\dfrac{4^6.9^5+6^9.120}{8^4.3^{12}-6^{11}}=\dfrac{2^{12}.3^{10}+2^9.3^9.2^3.3.5}{2^{12}.3^{12}-2^{11}.3^{11}}\)

\(=\dfrac{2^{12}.3^9.\left(1+3.5\right)}{2^{11}.3^{11}.\left(2.3-1\right)}=\dfrac{2.16}{3^2.5}=\dfrac{32}{45}\)

Chúc bạn học tốt!!!

a)25.5².1/625.5²

=5².5²/5⁴.5²

=5²

Hết biết nx !

, 4⁶.9⁵+6⁹.120 / 8⁴.3¹² - 6¹¹

mik mới lp 5 mí ??/??

Năm nay mình mới lên lp 4 nên không biết làm bài này.

Xin bạn thông cảm.