bai toán này kho lắm

tớ cũng đanh thắc mắc câu này

Bài 1 :

a/   \(a^3.a^9=a^{3+9}=a^{12}\)

b/\(\left(a^5\right)^7=a^{5.7}=a^{35}\)

c/  \(\left(a^6\right).4.a^{12}=a^{24}.a^{12}.4=a^{24+12}.4=a^{36}.4\)

d/  \(\left(2^3\right)^5.\left(2^3\right)^3=2^{15}.2^9=2^{15+9}=2^{24}\)

e/  \(5^6:5^3+3^3.3^2\)

     \(=5^3+3^5=125+243=368\)

i/ \(4.5^2-2.3^2\)

   \(=2^2.5^2-2.3^2\)

   \(=2^2.25-2^2.14\)

   \(=2^2.\left(25-14\right)\)

   \(=2^2.11\)      

   \(=4.11=44\)

Bài 2 :

a, \(3^8:3^6=3^{8-6}=3^2\)

 \(7^5:7^2=7^{5-2}=7^3\)

 \(19^7:19^3=19^{7-3}=19^4\)

  \(2^{10}.8^3=2^{10}.\left(2^3\right)^3=2^{10}.2^9=2^{19}\)  

\(12^7:6^7=\left(12:6\right)^7=2^7=128\)

\(27^5:81^3=\left(3^3\right)^5:\left(3^4\right)^3=3^{15}:3^{12}=3^3=9\)

Bạn Võ thị khánh ly ơi có thể giải giúp mk phần b bài 2 k

a: \(2^6\cdot3^3=\left(2^2\cdot3\right)^3=12^3\)

b: \(6^4\cdot8^3=2^4\cdot3^4\cdot2^9=2^{13}\cdot3^4\)

c: \(16\cdot81=36^2\)

d: \(25^4\cdot2^8=100^4\)

a) \(5^x:\left(5^2\right)^2=625\)

\(5^x:625=625\)

\(5^x=5^8\)=> x = 8

Mấy câu kia tương tự

d) \(\left(x-1\right)^4-\left(x-1\right)^4\cdot\left(x-1\right)^3=0\)

\(\left(x-1\right)^4\cdot\left[1-\left(x-1\right)^3\right]=0\)

\(\Rightarrow\orbr{\begin{cases}x-1=0\\\left(x-1\right)^3=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x-1=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}\)

Vậy,..........

làm rõ ra đi mà

\(18^{20}.45^5.5^{25}.8^{10}\)

\(=3^{40}.2^{20}.5^5.3^{10}.5^{25}.2^{30}\)

\(=3^{50}.2^{50}.5^{30}\)

\(=6^{50}.5^{30}\) 

\(=\left(6^5\right)^{10}.\left(5^3\right)^{10}\)

\(=\left(6^5.5^3\right)^{10}\)

\(\left(x^2y\right)^5.\left(x^2.y^2\right)^7.\left(x.y\right)^6.x^3\)

\(=x^{10}.y^5.x^{14}.y^{14}.x^6.y^3.x^3\)

\(=x^{33}.y^{22}\)

\(=\left(x^3\right)^{11}.\left(y^2\right)^{11}\)

\(=\left(x^3.y^2\right)^{11}\)

\(2^7.3^8.4^9.9^8\)

\(=2^7.3^8.2^{18}.3^{16}\)

\(=2^{25}.3^{24}\)( mk chỉ làm được đến thế thôi )

Tham khảo nhé~

a) \(18^{20}.45^5.5^{25}.8^{10}\)

\(=\left(2.3^2\right)^{20}.\left(3^2.5\right)^5.5^{25}.\left(2^3\right)^{10}\)

\(=2^{20}.3^{40}.3^{10}.5^5.5^{25}.2^{30}\)

\(=2^{50}.3^{50}.5^{30}\)

\(=6^{50}.5^{30}\)

\(=\left(6^5\right)^{10}.\left(5^3\right)^{10}\)

\(=7776^{10}.125^{10}\)

\(=972000^{10}\)

b ) \(\left(x^2y\right)^5.\left(x^2.y^2\right)^7.\left(xy\right)^6.x^3\)

\(=x^{10}.y^5.x^{14}.y^{14}.x^6.y^6.x^3\)

\(=x^{33}.y^{25}\)

\(=x^{25}.y^{25}.x^8\)

\(=...\)

c)  \(2^7.3^8.4^9.9^8\)

\(=2^7.3^8.\left(2^2\right)^9.\left(3^2\right)^8\)

\(=2^7.3^8.2^{18}.3^{16}\)

\(=2^{25}.3^{24}\)

\(=...\)( Câu c này hình như đề bài sai sót . Không chuyển thành lũy thừa được )

a) |x + 4| = 17

=> \(\orbr{\begin{cases}x+4=17\\x+4=-17\end{cases}}\)

=> \(\orbr{\begin{cases}x=13\\x=-21\end{cases}}\)

b) (7 - x) - (25 + 7) = -25

=> (7 - x) - 32 = -25

=> 7 - x = -25 + 32

=> 7 - x = 7

=> x = 7 - 7

=> x = 0

c. |x + 5| = |-7|

=> |x + 5 | = 7

=> \(\orbr{\begin{cases}x+5=7\\x+5=-7\end{cases}}\)

=> \(\orbr{\begin{cases}x=2\\x=-12\end{cases}}\)

2) 4 . (-5)² + 2 . (-15)

= 2. 2 . 25 + 2 . (-15)

= 2.(2 . 25 - 15)

= 2 . 35

= 70

1/ 

a) | x+4 | = 17

\(\Rightarrow\)x+4 = 17 hoặc x+4 = -17

        x      = 13         x      = -21

b) ( 7 - x ) - ( 25 + 7 ) = -25

     7 - x                      = -25 + 25 + 7

     7 - x                      = 7

          x                      = 0

c) | x + 5 | = 7

\(\Rightarrow\)x + 5 = 7 hoặc x + 5 = -7

         x        = 2         x        = -12

2/

    4 . ( -5 )² + 2 . ( -15 )

= 4 . 25 + 2 . ( -15 )

= 100 + ( -30 )

= 70

Hk tốt