In the expansion f (7^{1/3} + 11^{1/9})^{6561}, the number of terms free from radical is ?

General term,

Clearly, will be free from radical signs, if are integers for

∴ *r* = 0, 9, 18, 27, ...6561

0, 9, 18, ...6561 is in A.P.

First term, *a* = 0

Common – difference = 18 – 9 = 9

Last term, *t *= 6561

*l = a* + (*n –* 1)*d*, where *n *= number of terms

Hence, number of terms free from radical are 730.

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