We will give a summary of some results, including sum-product identities in terms of binary quadratic forms for powers k =2,3,4,5. These are akin to a "template" such that given just one integral solution to certain Diophantine equations of degree k, then an infinite more can be found and hence are useful in providing parametrizations of equal sums of like powers. There will also be Identities for higher powers found by other authors.
A limited quadratic forms version of Euler's Extended Conjecture will also be given.
