Verified answer

⁴√4st²(⁴√2s⁵t² + ⁴√s⁹t²)

The first steps are to pull all perfect 4th radicals from out of under the radical.

Examine ⁴√4st² and note that there's no perfect 4th radicals.

Next examine ⁴√2s⁵t² and notice that s⁵ is the same thing as s(⁴+¹) so s⁴ is a perfect 4th radical which can be pulled out:

s⁴√2st²

Next examine ⁴√s⁹t and note that s⁹ is the same thing as s(⁴+⁴+¹) so s² can be pulled out:

s² ⁴√st²

This becomes:

= ⁴√4st²(s ⁴√2st² + s² ⁴√st²)

Multiply the terms:

= (s ⁴√8s²t⁴) + (s² ⁴√4st² * ⁴√st²)

Continue pulling out perfect 4th roots as they are found:

= (st) ⁴√8s² + (s² ⁴√4st² * ⁴√st²)

Multiply terms again:

= st ⁴√8s² + (s² ⁴√4s²t⁴)

The t⁴ is a perfect 4th so it can be pulled out from under the radical:

= st ⁴√8s² + (s²t ⁴√4s²)

This becomes:

= (st ⁴√8s²) + (s²t ⁴√4s²)