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Maths indices help!

2^5/2 +2^1/2

It says the solution is: 2^2x2^1/2+2^1/2
4x2^1/2+2^1/2

Which I understand but then it says
5x2^1/2
=5 root 2

Where does the 5 come from?
Thank you!!
The way I would work it out would be by applying the indices rule: x^m/n = n root x^m

So in this case: 2^1/2 = square root 2^1 which is just sq. root 2

For 2^5/2 = square root 2^5 which is sq. root 32. This can be simplified to 4 root 2

Thus, if we add 4 root 2 and root 2, we got 5 root 2
Thank you so much!!

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