Hey guys, I'm just a bit unsure how to simplify numbers so that this induction can be proved. Any help would be appreciated.

$\displaystyle 2\frac{{[k(k+1)}]^{ 4} }{ 16} + {(k+1)}^{5 }+ {(k+1)}^{7 }= 2\frac{{[(k+1)(k+2)]}^{4 } }{ 16}$

Thanks. Hope the latex came out alright.