[tex]\sqrt[3]{54k^{7}p^{2}}[/tex] = [tex]\sqrt[3]{(2)(3)(3)(3)k^{6}(k)p^{2}}[/tex]
= [tex]3k^{2}[/tex] [tex]\sqrt[3]{2kp^{2}}[/tex]
Hence, the simplified form is [tex]3k^{2}[/tex] [tex]\sqrt[3]{2p^{2}}[/tex] .
