Bài $1$.
$a$) $4.5^3 - 17.2^4 + 35. 2020^0$
$= 4.5^3 - 17.2^4 + 35.1$
$= 4.125 - 17.16 + 35$
$= 500 - 272 + 35$
$= 263$.
$b$) $10^3 - {5^2 . 10 : [75 - (7-2)^2]}$
$= 1000 - [25.10 : (75-5^2)]$
$= 1000 - [250 : (75-25)]$
$= 1000 - (250 : 50)$
$= 1000 - 5$
$= 995$.
Bài $2$.
$a$) $390 - (x-7) = 169 : 13$
$⇔ 390 - (x-7) = 13$
$⇔ x - 7 = 377$
$⇔ x = 384$
Vậy $x=384$.
$b$) $(x-140):7 = 3^3 - 2^3 . 3$
$⇔ (x-140):7 = 27 - 8.3$
$⇔ (x-140) : 7 = 3$
$⇔ x - 140 = 21$
$⇔ x = 161$
Vậy $x=161$.
$c$) $3^{x+5} - 2. 3^{x+2} = 225$
$⇔ 3^{x+2} . 3^3 - 2 . 3^{x+2} = 225$
$⇔ 3^{x+2} . (3^3 - 2) = 225$
$⇔ 3^{x+2} . (27-2) = 225$
$⇔ 3^{x+2} . 25 = 225$
$⇔ 3^{x+2} = 9$
$⇔ 3^{x+2} = 3^2$
$⇔ x+2 = 2$
$⇔ x = 0$
Vậy $x=0$.
Bài $3$
$A = \dfrac{11 . 3^{22} . 3^7 - 9^{15}}{(2.3^{14})^2}$
$⇔ A = \dfrac{11 . 3^{29} - (3^2)^{15}}{2^2 . 3^{28}}$
$⇔ A = \dfrac{11.3^{29} - 3^{30}}{2^2 . 3^{28}}$
$⇔ A = \dfrac{3^{29} . (11 - 3)}{2^2 . 3^{28}}$
$⇔ A = \dfrac{3^{29} . 8}{2^2 . 3^{28}}$
$⇔ A = \dfrac{3^{29} . 2^3}{2^2 . 3^{28}}$
$⇔ A = \dfrac{3.2}{1} = 6$.
