1)
[tex]y^{10} = (....)^2[/tex]
Adopting: [tex] y^5[/tex]
[tex]y^{10} = (y^5)^2 [/tex]
[tex]y^{10} = y^{5*2}[/tex]
[tex]y^{10} = y^{10} (TRUE)[/tex]
Therefore (answer):
[tex]\boxed{\boxed{b) y^5}}[/tex]
2)
[tex]100h^{16} = (....)^2[/tex]
Adopting: [tex]10h^8[/tex]
[tex]100h^{16} = (10h^8)^2 [/tex]
[tex]100h^{16} = 100h^{8*2}[/tex]
[tex]100h^{16} = 100h^{16} (TRUE)[/tex]
Therefore (answer):
[tex]\boxed{\boxed{a) 10h^8}}[/tex]