[tex]a)~x^{5}*x^{7}=x^{5+7}=x^{12}[/tex]
[tex]b)~\frac{a^{7}*a^{3}}{a^{2}}=\frac{a^{7+3}}{a^{2}}=\frac{a^{10}}{a^{2}}=a^{10}:a^{2}=a^{10-2}=a^{8}[/tex]
[tex]c)~(-4y)^{2}*(4y^{3})=4^{2}*y^{2}*4^{1}*y^{3}=4^{2+1}*y^{2+3}=4^{3}*y^{5}=(2^{2})^{3}*y^{5}=2^{2*3}*y^{5}=2^{6}*y^{5}[/tex]
[tex]d)~a^{9}b^{3}*(\frac{b^{4}}{a^{2}})^{2}=a^{9}b^{3}*\frac{(b^{4})^{2}}{(a^{2})^{2}}=a^{9}b^{3}*\frac{b^{8}}{a^{4}}=a^{9}*b^{3}*b^{8}:a^{4}=a^{9-4}*b^{3+8}=a^{5}*b^{11}[/tex]
