Lời giải:

Dãy trên là dãy cách đều với khoảng cách = 8

Số thứ 110 là: $(110-1)\times 8+144=1016$

Tổng của 110 số hạng đầu tiên: 

$(1016+144)\times 110:2=63800$

a) \(7^3.7^5=7^{3+5}=7^8\)

b)\(5^6.5^4=5^{6+4}=5^{10}\)

\(\left(x-36\right):\left(2.3^2\right)=2^2.3\)

\(\Rightarrow\left(x-36\right):18=12\)

\(\Rightarrow\left(x-36\right)=12.18\)

\(\Rightarrow x-36=216\)

\(\Rightarrow x=216+36\)

\(\Rightarrow x=252\)

(x-36):(2.3²)=2.2³

⇒ (x-36):(2.9)=2.8

⇒ (x-36):18=16

⇒ x-36=18.16=288

⇒ x=288+36=324

1574+(625-x)=2023

⇒ 625-x=2023-1574=449

⇒ x=625-449=176

Vậy x=176

1574 + (625 - x) = 2023

625 - x = 2023 - 1574

625 - x = 449

x = 625 - 449

x = 176

\(148+144+140+...+56+52\)

\(=\left[\left(148-52\right):4+1\right]\left(148+52\right):2\)

\(=25.200:2=25.100=2500\)

$148+144+140+...+56+52$

$=\left[\left(148-52\right):4+1\right]\left(148+52\right):2$

$=25.200:2=25.100=2500$

\(\left(x-257\right)-921=2^5\)

\(x-257=32+921\)

\(\)\(x-257=953\)

\(x=953+257\)

\(x=1210\)

\(\left(x-257\right)-921=2^5\)

\(\Rightarrow x-1178=32\Rightarrow x=32+1178=1210\)

a) \(...=-246+301=55\)

b) \(...=-\dfrac{10}{9}+\dfrac{5}{12}=-\dfrac{40}{36}+\dfrac{15}{36}=-\dfrac{25}{36}\)

c) \(...=-\dfrac{3}{26}+\dfrac{24}{69}=-\dfrac{207}{1794}+\dfrac{624}{1794}=\dfrac{417}{1794}\)

\(\dfrac{\left(\dfrac{2}{7}\right)^7.7^7+\left(\dfrac{9}{4}\right)^3:\left(\dfrac{3}{16}\right)^3}{2^7.5^2+512}\)

\(=\dfrac{\dfrac{2^7}{7^7}.7^7+\left(\dfrac{9}{4}:\dfrac{3}{16}\right)^3}{2^7.5^2+2.256}\)

\(=\dfrac{2^7+\left(\dfrac{9}{4}.\dfrac{16}{3}\right)^3}{2^7.5^2+2.2^8}=\dfrac{2^7+\left(12\right)^3}{2^7.5^2+2.2^8}\)

\(=\dfrac{2^7+\left(2^2.3\right)^3}{2^7.5^2+2^9}=\dfrac{2^7+2^6.3^3}{2^7.\left(5^2+2^2\right)}\)

\(=\dfrac{2^6\left(2+27\right)}{2^7.\left(25+4\right)}=\dfrac{29}{2.29}=\dfrac{1}{2}\)