Đáp án:

Bài 1:
$a) 2.2.2.3.3.5.5\\
b) 2.2.2.3.5\\
c) 73$
Bài 2:
$a) x=2\\
b)  x=15$
c)  $x=\{-2,-4,0,2\}$
d) $ x=\{60,70,80,90\}$
Bài 3: 370 học sinh

Giải thích các bước giải:

Bài 1:
$a) 5.18.7+18.65=18(5.7+65)=18.(35+65)=18.100=1800=2.2.2.3.3.5.5\\
b) 150-(3^2-5.3)=150-3.5(3-1)=150-15.2=150-30=120=2.2.2.3.5\\
c) 2^3.3^2+32:2^5=2^3.3^2+2^5:2^5=2^3.3^2+1=8.9+1=73$
Bài 2:
$a) (x+3)^3=125\\
\Leftrightarrow x+3=\sqrt[3]{125}=5\\
\Leftrightarrow x=5-3=2\\
b) (2x-3^2).7^6=7^7.3\\
\Leftrightarrow 2x-3^2=\frac{7^7.3}{7^6}=7.3=21\\
\Leftrightarrow 2x=21+3^2=21+9=30\\
\Leftrightarrow x=15\\
c) x+4 =(x+1)+3\vdots x+1\Leftrightarrow 3\vdots x+1\\
\Rightarrow x \in U(3)=\{-1,-3,1,3\}\\
\Rightarrow x+1=-1\Rightarrow x=-2\\
x+1=-3\Rightarrow x=-4\\
x+1=1\Rightarrow x=0\\
x+1=3\Rightarrow x=2$
Vậy $x=\{-2,-4,0,2\}$
d) $x\vdots 2,x\vdots 5\Rightarrow x\in BCNN(2,5)=2.5=10\\
\Rightarrow B(10)=\{0,10,...,50,60,70,80,90,100,...\}$
Vì $60 \leq x \leq 90\Rightarrow x=\{60,70,80,90\}$
Bài 3:
Gọi x là số học sinh khối 6 $(x\in \mathbb{N}^*)$
Khi xếp hàng 12,15,36 đều thừa 10 em tức $x-10 \vdots 12,15,36$
Ta có 
$12=2^2.3\\
15=3.5\\
36=2^2.3^2\\
\Rightarrow BCNN(12,15,36)=2^2.3^2.5=180\\
\Rightarrow x-10 \in B(180)=\{0,180,360,540,...\}\\
x=\{10,190,370,550,....\}$
Vì $300 \leq x\leq 400\Rightarrow x=370$