$a)\frac{3}{{\sout{4}}^1}\cdot {\sout{12}}^3=9$

$b)3\frac{2}{3}\cdot 12=\frac{11}{{\sout{3}}^1}\cdot {\sout{12}}^4=44$

$c)\frac{7}{{\sout{10}}^1}\cdot {\sout{60}}^6=42$

$d)5\frac{1}{5}\cdot 60=\frac{26}{{\sout{5}}^1}\cdot {\sout{60}}^{12}=26\cdot 12=26\cdot \left(10+2\right)=26\cdot 10+26\cdot 2=260+52=312$