(a) Simplify \(\sqrt{x^8y^{10}}\div\sqrt[3]{x^3y^{-6}}\), giving your answer in the form \(x^ay^b\), where \(a\) and \(b\) are integers.

(b)(i) Show that \(4(t-2)^{1/2}+5(t-2)^{3/2}\) can be written in the form \((t-2)^p(qt+r)\), where \(p\), \(q\), and \(r\) are constants to be found.

(b)(ii) Hence solve \(4(t-2)^{1/2}+5(t-2)^{3/2}=0\).