what is 27^1/2

Sqrt 27= 3root3 in surd form. Easier to keep in this form while you are working through a problem,ie solving a triangle.

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!

$${{\mathtt{27}}}^{{\mathtt{0.5}}} = {\mathtt{5.196\: \!152\: \!422\: \!706\: \!631\: \!9}}$$

$${{\mathtt{27}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\sqrt{{\mathtt{27}}}}$$            =>    $${\sqrt{{\mathtt{27}}}} = {\mathtt{5.196\: \!152\: \!422\: \!706\: \!631\: \!9}}$$

Rosala, it is very easy to get confused with this stuff.

Remember, fractional indices are roots AND roots are NOT the same as dividing.

I will give you 3 points for having a go.