<PRE><B>Question 208136</B>
{{{(w+3)^(-1/3) = 1/3}}}
:
Reciprocal gets rid of the negative exponent
{{{1/((w+3)^(1/3)) = 1/3}}}
:
Multiply both side by 3
{{{3/((w+3)^(1/3)) = 1}}}
:
Cube both sides:
{{{27/((w+3)) = 1}}}
:
27 = w + 3
:
w = 24
:
:
Check solution on calc: enter {{{(24+3)^(-1/3)}}} = .333
;
;
;
{{{(x+2)^(3/2)}}} = -1
:
Square both sides
{{{(x+2)^3}}} = +1
: 
Find the cube root of both sides:
x + 2 = 1
:
x = 1 -2
x = -1
The problem here is if you substitute -1 for x in the original equation,
you get +1 not -1, so there is no solution here</PRE>