Evaluate following.

(a) 625^3/4

Solution

 (a) 625^3/4

Again, let's employ both forms to calculate this one.

            625^3/4   =( 625^1/4 )³ =(5)³  = 125           625^1/4  = 5  because  5⁴  = 625

             625^3/4  = (625³ )^1/4   = ( 244140625)^1/4   = 125   because 125⁴  = 244140625

As this part has illustrated the second form can be quite hard to employ in computations. The root in this case was not an apparent root and not specifically easy to get if you didn't know it right off the top of your head.