Radical form?

Question

I'm so confused about this, how do I know that my answer is in radical form? 

for example 

 

a) ⁴√(32w⁸)

 

 

the answers that I'm getting is

 

 

2⋅2^1/4w²  is this radical form?

 

 

 

 

 

 

Answer 1

 

EXAMPLE:  the fourth root of 16,  ⁴√16 = ⁴√2^.2^.2^.2

      Since there are 4 factors of 2 (4 2's under the radical), they can be removed from under the radical and placed in

      front of it as a single 2.  There's nothing left under the radical so it can go away, leaving only the 2, which you

      know already that the fourth root of 16 is 2.

 

EXAMPLE:  the cube root of 32x⁷ = ³√2^.2^.2^.2^.2^.x^.x^.x^.x^.x^.x^.x = 2^.x^.x^. 3√(2^.2^.x) = (2x²⁾_*³√(4x)

  1 set of 3 2's under radical => mark out 3 2's and place one 2 in front of the radical

  2 sets of 3 x's under radical => mark out TWO sets of 3 x's and put TWO x's in front of the radical

  Multiply what's in front of the radical (one 2 and 2 x's = 2x² and then what's left under the radical

       (2 2's and an x = 4x) to get:   two x squared times the cube root of 4x) 

 

With those concepts in mind,

 

⁴√(32w⁸) = ⁴√(2*2*2*2*2*w*w*w*w*w*w*w*w) = 2*w*w_*⁴√2 = 2w²_*⁴√2

Answer 2

Your answer is correct, but  "radical form" means with a radical (√) instead of an exponent.  So 2*2^1/4*w² should be 2w^{2 4}√2.  But good job on getting the right answer!