The total number of irrational terms in the binomial  expansion of ${\left(7^{1/5}-3^{1/10}\right)}^{60}$ is 

Given expression is ${ }_{ }{\left(7^{1/5}-3^{1/10}\right)}^{60}$

General terms of this expansion is $T_{r+1}=(-1{)}^r\left({ }^{60}{C}_r {\left(7^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$5$}\right.}\right)}^{60-r}{\left({\stackrel{ }{ 3}}^{\frac{1}{10}}\right)}^r\right)$

For rational terms $r=0,10,20,30,40,50,60$

So, number of rational terms = 7

$\therefore$Number of irrational terms = 61 -7 =54