Question 1013852
<pre>
There are two solutions. The other tutor did not get both solutions.
I'll go into a little more detail.

{{{matrix(2,3,"","","",
(z+4)^(4/5),""="",2)}}}

Raise both sides of the equation to the reciprocal of {{{4/5}}}
power, which is the {{{5/4}}} power:

{{{matrix(2,3,"","","",
((z+4)^(4/5))^(5/4),""="",2^(5/4))}}}

Remove the parentheses on the left by multiplying the exponents 
which just gives the exponent 1.

On the right we use the rule: {{{matrix(2,3,"","","",
b^(m/n),""="",root(n,b^m))}}}

But since the root we are taking is even, the fourth root,
there are two fourth roots, positive and negative, so we must
precede it by ±:


{{{matrix(2,3,"","","",
(z+4)^1,""="","" +- root(4,2^5))}}}

{{{matrix(2,3,"","","",
z+4,""="",root(4,2^4*2^1))}}}

{{{matrix(2,3,"","","",
z+4,""="","" +- 2*root(4,2^1))}}}

{{{matrix(2,3,"","","",
z+4,""="","" +- 2*root(4,2))}}}

{{{matrix(2,3,"","","",
z,""="","" +- 2*root(4,2)-4)}}}

So there are two solutions, 

{{{matrix(2,3,"","","",
z,""="",2*root(4,2)-4)}}} and {{{matrix(2,3,"","","",
z,""="",-2*root(4,2)-4)}}}

Edwin</pre>