Evaluate following.
(a) 625^{3/4}
Solution
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 5^{4} = 625
625^{3/4 }= (625^{3} )^{1/4} = ( 244140625)^{1/4} = 125 because 125^{4} = 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.