Câu `1`:

`729 = 9^3 = 3^6 = 27^2`

Câu `2:`

`2^5 . 8^4 = 2^5 . (2^3)^4 = 2^5 . 2^12 = 2^17`

`25^6 . 125^3 = (5^2)^6 . (5^3)^3 = 5^12 . 5^9 = 5^21`

`625^5 : 25^7 = (5^4)^7 : (5^2)^7 = 5^28 : 5^14 = 5^14`

`12^3 . 3^3 = (12 . 3)^3 = 36^3`

Câu `3`:

`6^(3^1) = 6 . 6 . 6 = 216`

`3^(2^3) = 3 . 3 . 3 . 3 . 3 . 3 . 3 . 3= 6561`

`7^(1^(2^(3^4))) = 7 . 1 = 7`

`2003^2^0^1^0 = 2003^1`

Câu `4`:

`2^x - 15 =17`

`=> 2^x = 17 + 15`

`=> 2^x = 32`

`=> 2^x = 2^5`

`=> x = 5`

Vậy `x = 5`

`(7 . x - 11)^3 = 2^5 . 5^2 + 200`

`=> (7 . x - 11)^3 = 1000`

`=> (7 . x - 11)^3 = 110^3`

`=> 7 . x - 11 = 10`

`=> 7 . x = 10 + 11`

`=> 7 . x = 21`

`=> x = 3`

Vậy `x = 3`

Câu `5`:

`x^10 = 1^x`

`=> x^10 = 1`

`=> x = 1 ; 0`

Vậy `x = 0 ; 1`

`x^10 = x`

`=> x^10 - x = 0`

`=> x = 0 ; 1`

Vậy `x = 0 ; 1`

`(2 . x - 15)^5 = (2 . x - 15)^3`

`=> (2 . x - 15)^5 = 1`

`=> 2x - 15 = 1`

`=> 2x = 16`

`=> x = 8`

Vậy `x = 8`

Câu `6`:

Câu 1:

`729 = 3^6`

`729 = 9^3`

`729 = 27^2`

Câu 2:

a. `2^5 × 8^4 = 2^5 × 2^12 = 2^17`

b. `25^6 × 125^3 = 125^4 × 125^3 = 125^7`

c. `625^5 : 25^7 = 25^10 : 25^7 = 25^3`

d. `12^3 × 3^3 = 36^3`

Câu 3:

a. `6^(3^1) = 6^3 = 216`

b. `3^(2^3) = 3^8 = 6561`

c. `7^(1^(2^(3^4))) = 7^1 = 7`

d. `2003^(2^(0^(1^0))) = 2003^(1^1) = 2003`

Câu 4:

a.

`2^x - 15 = 17`

`⇔2^x = 32`

`⇔2^x = 2^5`

`⇒x = 5`

b.

`(7x - 11)^3 = 2^5 × 5^2 + 200`

`⇔(7x - 11)^3 = 800 + 200`

`⇔(7x - 11)^3 = 1000`

`⇔(7x - 11)^3 = 10^3`

`⇔7x - 11 = 10`

`⇔7x = 21`

`⇔x = 3`

Câu 5:

a.

`x^10 = 1^x`

`⇔x^10 = 1`

`⇔`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\) 

Vậy `(x, y) = (0; 1)`

b.

`x^10 = x`

`⇔x^10 - x = 0`

`⇔`\(\left[ \begin{array}{l}x=0\\x=1\end{array} \right.\) 

Vậy `(x, y) = (0; 1)`

c.

`(2x - 15)^5 = (2x - 15)^3`

`⇔(2x - 15)^2 = 1`

`⇔2x - 15 = 1`

`⇔2x = 16`

`⇔x = 8`

Vậy `x = 8`

Câu 6:

`A=(11*3^22*3^7-9^15)/((2*3^14)^2)`

`=(11*3^29-9^15)/(2^2*3^38)`

`=(11*3^29-3^30)/(2^2*3^28)`

`=(11*3^29-3^29*3)/(4*3^28)`

`=((11-3)*3^29)/(4*3^28)`

`=(8*3^29)/(4*3^28)`

`=(8*3)/4=6`

Vậy `A = 6`