Question

In the expansion of $(5^{\frac{1}{3}}-8^{\frac{1}{7}}{)}^{1126}$, the number of integral terms is

Answer 1

For the expansion ${}^{1126}Cr{5}^{(1126-r)/3}{8}^{r/7}$
$1126-r$ should be a multiple of $3$
$r=1,4,7,10,.....1123$
Also $r$ should be a multiple of $7$
$r=7,14,21,28,1120$
L.C.M of $3$ and $7$ will be $21$
First term is $7$ then with the difference of $21$ making and A.P.
$1120=7+(n-1)21$
$n=54$