Does there exist a primitive pythagorean triple $(a, b, c)$ with $a$ and $b$ are perfect powers (bigger than one)?

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I am not able to find any such triple, only find infinitely many triples with one of it is a perfect power.

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A multiple of 3,4,5 gives: 27,36,45.

That is, $(3^3)^2+(6^2)^2=45^2$.

In some generality, if you have a Pythagorean triple $(a,b,c)$ where $b=d^\ell$, then $(a^{\ell+1}, (ad)^\ell, c\cdot a^\ell)$ seems to be a triple of the form you want.