(i) Prime factorization of 64 is as follows:

= 2 x 2 x 2 x 2 x 2 x 2

Hence,

= 4

(ii) Prime factorization of 512 is as follows:

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

Hence,

= 8

(iii) Prime factorization of 10648 is as follows:

= 2 x 2 x 2 x 11 x 11 x 11

Hence,

= 22

(iv) Prime factorization of 27000 is as follows:

= 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

Hence,

= 30

(v) Prime factorization of 15625 is as follows:

= 5 x 5 x 5 x 5 x 5 x 5

Hence,

= 25

(vi) Prime factorization of 13824 is as follows:

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Hence,

= 24

(vii) Prime factorization of 110592 is as follows:

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

Hence,

= 48

(viii) Prime factorization of 46656 is as follows:

= 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

Hence,

= 36

(ix) Prime factorization of 175616 is as follows:

= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 7 x 7 x 7

Hence,

= 56

(x) Prime factorization of 91125 is as follows:

= 3 x 3 x 3 x 3 x 3 x 3 x 5 x 5 x 5

Hence,

= 45