# How to simplify polynomial at my Taylor series ?

Posted 1 month ago
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 The following formula u^6 Sqrt[u^3 ], how to simplify to \ u^(15/2)  Attachments: Answer
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Posted 1 month ago
 t1 = u^6 Sqrt[u^3] {t1, (1/t1)} /. { Power[Power[u_, n_], Rational[p_, m_]] -> Power[u, (p n)/m]} Answer
Posted 1 month ago
 Hi, Michael Thank you for your code . How can I show the function like that  Answer
Posted 1 month ago
 Hope this helps. I used E2 etc instead of Eunderscore2 t2 = carlson[E2, E3] /. {Power[Power[u_, n_], Rational[p_, m_]] -> Power[u, ( p n)/m]} // Normal // Collect[#, {u}] & Answer
Posted 1 month ago
 Hello Thank you for your code again. How to put u^(3/2) at first item ,u^(7/2) at 2nd item,...u^(23/2) at last item, Answer
Posted 1 month ago
 I am not sure that I understand exactly what you are intended to do but you can pull the polynomial expression apart. First you temporarily replace the u by a variable v with positive integer exponents: t3 = t2 /. Power[ u_, Rational[p_, m_]] -> Power[v, -(p/m + 1/2)] Now you use CoefficientList to extract the coefficients: t4 = CoefficientList[t3, {v}]; Finally you bring back u into a separate list. The result looks like t5 = {v^Range[0, Length[t4] - 1] /. {Power[v, n_] -> Power[u, -n - 1/2], v -> u^(-3/2)}, t4} Here is a check that this decomposition corresponds in fact to T2 Total[Map[Apply[Times, #] &, t5\[Transpose]]] == t2 Hope that helps Answer
Posted 1 month ago
 Michael, thank you again. You had shooting my all problem. How can I study those setting ? Do you have web sit or book else. Answer