As you have writtem 27^1 without brackets it has various meanings!lets see!
1.
having a power of $$\frac{1}{2}$$ means that a number has been brought to normal form turning its
"square root" look to a simple one!
ive learnt it this way.....
so we can change yours to √27 which makes 27^1/2
(i just want some moderator help..i have learnt it this year....but i just havnent got the right words)
2.
(27^1)/2
now having a power of 1 means the number will remain unmultiplied.
so
27/2
= 13.5
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so those were the two ways.....
I have edited this answer after seeing Radix's ones and remembering the rigth thing!
$${{\mathtt{27}}}^{{\mathtt{0.5}}} = {\mathtt{5.196\: \!152\: \!422\: \!706\: \!631\: \!9}}$$
$${{\mathtt{27}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\sqrt{{\mathtt{27}}}}$$ => $${\sqrt{{\mathtt{27}}}} = {\mathtt{5.196\: \!152\: \!422\: \!706\: \!631\: \!9}}$$
.