How to select p terms with powers larger than 1 in a given expression?

My expression is:

expr = (p^(1/3) q + 5)/(3q^2)+p^2+(p-1)^(1/3)

And I want to single out all terms with $$p^k, k > 1$$

How should I do that? (If there is any way other than applying Series[] would be the best, since I want it to be less time-consuming when dealing with large expr.)

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• Please give your expression in code. This will make it easier for others to help you out. Sep 12 '21 at 5:05

And I want to single out all terms with p^k,k>1

I use this nice function getPatterns thanks to Carl Woll that he gave me as an answer long time ago. It is a handy function to have in your toolbox.

ClearAll[p, q];
expr=(p^(1/3)*q+5)/(3*q^2)+p^2+(p-1)^(1/3)+p^5+(p^(9/2)-1)^(1/3) getPatterns[expr_, pat_] := Last@Reap[expr /. a : pat :> Sow[a], _, Sequence @@ #2 &];

And now

getPatterns[expr, Power[p, x_] /; x > 1] Edit

if there is a term 2 q p^(1/3), it only gives p^(1/3) while neglecting 2 q factor in front under current setting. And I want to have the final answers attached with 2 q factor

You can change the pattern to

expr = (2 *q*p^(1/3)*q + 5)/(3*q^2) + p^2 + (p - 1)^(1/3) +
p^5 + (888*p^(1/2) - 1)^(1/3)
getPatterns[expr, any_*Power[p, x_] /; x < 1] • Thank you for your reply! But is there anyway to also single out the coefficients corresponding to the terms? Sep 12 '21 at 5:29
• @TianyiWang You mean the actual powers themselves? Sep 12 '21 at 5:30
• For example, if there is a term 2 q p^(1/3), it only gives p^(1/3) while neglecting 2 q factor in front under current setting. And I want to have the final answers attached with 2 q factor. Sep 12 '21 at 5:36
• @TianyiWang please see edit. Sep 12 '21 at 5:41
• It works!! Thanks a lot! Sep 12 '21 at 6:12