The number of words which can be obtained by arranging the letters of the word INTERMEDIATE, so that no two vowels are together, is 

The consonants DMNRTT can be arranged in 

$\frac{6!}{2!}=360$ ways

The vowels AIIEEE can be arranged in the seven places adjacent to the consonants is $\left(\begin{array}{l}7\\ 6\end{array}\right)\frac{6!}{2!3!}=42$0 ways

The desired number is  $360\times 420=151200$