Numerical Morphisms

A number num, that elevated to the power of another number k "ends" with the same num, it's automorphic.

5² = 25
// It's automorphic because "25" ends with "5"

5³  = 125
// It's automorphic because "125" ends with "5"

76⁴ = 33362176
// It's automorphic because "33362176" ends with "76"

A number can have various powers that make it automorphic (i.e. look at number 5 in the above example). In this challenge, you have to verify if the given number is automorphic for each power from 2 up to 10.

Given a non-negative integer num, implement a function that returns the string:

• "Polymorphic" if num is automorphic for every power from 2 up to 10.
• "Quadrimorphic" if num is automorphic for only four powers (any from 2 up to 10).
• "Dimorphic" if num is automorphic for only two powers (any from 2 up to 10).
• "Enamorphic" if num is automorphic for only one power (any from 2 up to 10).
• "Amorphic" if num is not automorphic for for any powers from 2 up to 10.

Examples

powerMorphic(5) ➞ "Polymorphic"
// From 2 up to 10, every power of 5 ends with 5

powerMorphic(21) ➞ "Enamorphic"
// 21⁶ = 85766121

powerMorphic(7) ➞ "Dimorphic"
// 7⁵ = 716807
// 7⁹ = 40353607

powerMorphic(4) ➞ "Quadrimorphic"
// 4³ = 64
// 4⁵ = 1024
// 4⁷ = 16384
// 4⁹ = 262144

powerMorphic(10) ➞ "Amorphic"
// There are no powers that make it automorphic

Notes

• You can do a complete loop cycle to check if num is automorphic for each power, or you can try to spot the discriminants that permit you to shorten the logic of your code.
• Despite being inspired by the OEIS sequence A003226, the assertions of this challenge are to be considered properly valid only in the specific context.
• Note for JavaScript: the inputs will be given as BigInt (big integers) to avoid approximation errors but, besides the numbers notation, there are no differences in the procedure to adopt.