Simplify 4 times the 4th root of 48.

That could be re-written as:

4(3*16)^(1/4), where (1/4) represents "fourth root," and 16 is a perfect 4th power whose fourth root is 2.  

Thus, we get 4 [ 3^(1/4) * 2 ] = 8*3^(1/4), or
                                                  8 times the fourth root of 3.

Logical equivalent of the give question is its contrapositive