(5^0.25) x (125^0.25) / (256^0.10) x (256^0.15) = ?

5^0.25 x 125^0.25 = (5 * 125)^0.25  [a^mXb^m = (ab)^m]

= 625^0.25

= (5⁴)  ^0.25

=  5^4*  0.25  [(a^m)ⁿ= (a)^mn]

= 5¹

= 5

(256^0.10) x (256^0.15) = 256 ^(0.10+0.15)  (a^m * aⁿ = a^m+n)

= (256) ^0.25

= (4⁴)^0.25

= 4 ^4*0.25  [(a^m)ⁿ= (a)^mn]

= 4¹

= 4

So,

(5^0.25) x (125^0.25) / (256^0.10) x (256^0.15) = 5/4