Swap prime exponents with their neighbours
Jelly, 10 bytes

ÆE;0s2UFÆẸ


Try it online! or verify all test cases.

How it works

ÆE;0s2UFÆẸ  Main link. Argument: n

ÆE          Yield the exponents of n's prime factorization.
  ;0        Append a zero.
    s2      Split into pairs.
      U     Upend; reverse each pair.
       F    Flatten the resulting list of pairs.
        ÆẸ  Convert the prime exponents to integer.