Question 912667
The exponents sometimes are rendered difficult to read, so some comments are included.


{{{(8+2x)^(5/4)=32}}} as you found before struggling.


{{{(2x+8)^(5/4)=2^5}}}, commutative for addition.  Also 32 is a power of 2.


{{{((2x+8)^(5/4))^(4/5)=(2^5)^(4/5)}}}, which should present no complications for signs; raising both sides to the four-fifths power.



{{{(2x+8)^1=2^((5)(4/5))}}},  power on left side is 1 and power on the right side is five multiplied by four-fifths.


{{{highlight_green(2x+8=2^4)}}}-----This should now be easy to finish.