Verified answer

[tex]\displaystyle\bf\\\frac{4^{6}\cdot 2^{9} }{32^{4} } =\frac{(2^{2})^{6} \cdot 2^{9} }{(2^{5} )^{4} } =\frac{2^{12}\cdot 2^{9} }{2^{20} } =\frac{2^{12+9} }{2^{20} } =\frac{2^{21} }{2^{20} } =2^{21-20}=2[/tex]