the fourth root of 7 to the fifth power

$${{\mathtt{7}}}^{\left({\frac{{\mathtt{5}}}{{\mathtt{4}}}}\right)} = {\mathtt{11.386\: \!035\: \!931\: \!884\: \!500\: \!2}}$$

or

$${\left({{\mathtt{7}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{5}}}}\right)} = {\mathtt{1.102\: \!186\: \!029\: \!687\: \!850\: \!4}}$$

Depends whether a 5th power is a power of 5 or a power of 1/5

I'd go for the first one but there is room for confusion - What do other mathematicians think?

The first one, for sure. The second is the fifth root of the fourth root of 7.

Thanks Chris but I still think that this terminology is very confusing.

I'd call it a power of 5 or a power of 1/5 or the fifth root !

Talking about the 5th power is just too confusing!