Powers

We can rewrite the number as follows

${ 4 }^{ 16 }{ 5 }^{ 25 }={ 2 }^{ 32 }{ 5 }^{ 25 }={ 2 }^{ 7 }{ 10 }^{ 25 }$

We know ${ 10 }^{ 25 }$ has 26 digits and multiplying by ${ 2 }^{ 7 }=128$ will add two more to that, so all in all there are 28 digits