Câu $1$.
$\dfrac{114}{122} = \dfrac{57}{61} = \dfrac{57.101}{61.101} = VP$
Vậy $\dfrac{114}{122} = \dfrac{5757}{6161}$.
Câu $2$.
$a$) $\dfrac{3^{10} . (-5)^{21}}{(-5)^{20} . 3^12}$
$= \dfrac{1 . (-5)}{1 . 3^{2}}$
$= \dfrac{-5}{9}$
$b$) $\dfrac{-11^{5} . 13^{7}}{11^5 . 13^8}$
$= \dfrac{-1.1}{1.13}$
$= \dfrac{-1}{13}$
$c$) $\dfrac{2^{10} . 3^{10}}{2^{10} . 3^9}$
$= \dfrac{1.3}{1.1}$
$= 3$
$d$) $\dfrac{5^{11} . 7^{12} + 5^{11} . 7^{11}}{5^{12}.7^{12} + 9.5^{11}.7^{11}}$
$= \dfrac{5^{11}.7^{11}.(7+1)}{5^{11}.7^{11}.(5.7+9)}$
$= \dfrac{8}{44}$
$= \dfrac{2}{11}$.