Sau khi giảm giá số tiền cần trả là:

     \(\left(200+350\right).20\%=110\) ( nghìn đồng )

Số tiền được giảm:

(200000 + 350000) . 20% = 110000 (đồng)

Số tiền bạn Hạnh phải trả:

200000 + 350000 - 110000 = 440000 (đồng)

\(7-(x-1,2)^2=4\\\Rightarrow (x-1,2)^2=7-4\\\Rightarrow (x-1,2)^2=3 \\\Rightarrow \left[\begin{array}{} x-1,2=\sqrt3\\ x-1,2=-\sqrt 3 \end{array} \right. \\\Rightarrow \left[\begin{array}{} x=1,2+\sqrt3\\ x=1,2-\sqrt3 \end{array} \right.\)

a) Thể tích hồ cá là:

$2\cdot 1,2\cdot 1,5=3,6(m^3)$

Diện tích xung quanh hồ cá là:

$2(2+1,2)\cdot 1,5=9,6(m^2)$

b) Bạn xem lại đề nhé!

Ta có:

\(\left(-16\right)^{11}=-16^{11}=-\left(2^4\right)^{11}=-2^{4\cdot11}=-2^{44}\)

\(\left(-32\right)^9=-32^9=-\left(2^5\right)^9=-2^{5\cdot9}=-2^{45}\)

Mà: \(44< 45\)

\(\Rightarrow2^{44}< 2^{45}\)

\(\Rightarrow-2^{44}>-2^{45}\)

${\left(-16\right)}^{11}=-16^{11}=-{\left(2^4\right)}^{11}=-2^{4\cdot 11}=-2^{44}$

${\left(-32\right)}^9=-32^9=-{\left(2^5\right)}^9=-2^{5\cdot 9}=-2^{45}$

Mà                 44<4544<45

$\Rightarrow 2^{44}<2^{45}$

$\Rightarrow -2^{44}>-2^{45}$

\(3^{1001}\cdot\left(5+2x\right)=3^{999}\)

\(\Rightarrow5+2x=\dfrac{3^{999}}{3^{1001}}\)

\(\Rightarrow5+2x=\dfrac{1}{3^2}\)

\(\Rightarrow5+2x=\dfrac{1}{9}\)

\(\Rightarrow2x=\dfrac{1}{9}-5\)

\(\Rightarrow2x=-\dfrac{44}{9}\)

\(\Rightarrow x=-\dfrac{44}{9}:2\)

\(\Rightarrow x=-\dfrac{22}{9}\)

\(3^{1001}.\left(5+2x\right)=3^{999}\)

\(\Rightarrow5+2x=\dfrac{3^{999}}{3^{1001}}\)

\(\Rightarrow5+2x=\dfrac{1}{3^2}\)

\(\Rightarrow5+2x=\dfrac{1}{9}\)

\(2x=\dfrac{1}{9}-5\)

\(x=-\dfrac{44}{9}:2\)

\(x=-\dfrac{22}{9}\)

\(\dfrac{5}{4}-\dfrac{1}{4}\left(x-\dfrac{2}{3}\right)=\dfrac{5}{2}\\ =>\dfrac{1}{4}\left(x-\dfrac{2}{3}\right)=\dfrac{5}{4}-\dfrac{5}{2}=-\dfrac{5}{4}\\ =>x-\dfrac{2}{3}=-\dfrac{5}{4}:\dfrac{1}{4}=-5\\ =>x=-5+\dfrac{2}{3}=-\dfrac{13}{3}\)

a)

\(3^{21}-3^{18}\\ =3^{17}.\left(3^4-3\right)\\ =3^{17}.\left(81-3\right)\\ =3^{17}.78\)

Vì \(3^{17}.78⋮78\) nên \(3^{21}-3^{18}⋮78\) (đpcm)

Vậy...

b)
\(81^7-27^9-9^{13}\\ =\left(3^4\right)^7-\left(3^3\right)^9-\left(3^2\right)^{13}\\ =3^{28}-3^{27}-3^{26}\\ =3^{24}.\left(3^4-3^3-3^2\right)\\ =3^{24}.\left(81-27-9\right)\\ =3^{24}.45\)

Vì \(3^{24}.45⋮45\) nên \(81^7-27^9-9^{13}⋮45\) (đpcm)

Vậy...

\(2^{n+1}=2^3\)

\(\Rightarrow n+1=3\)

\(\Rightarrow n=3-1\)

\(\Rightarrow n=2\)

Vậy: n=2