Question 981158
<pre>
{{{matrix(2,3, "","","",
             8^(5/3),""="",2^(4x/2))}}}

Simplify the exponent {{{(4x)/2}}} as just {{{2x}}}

{{{matrix(2,3, "","","",
             8^(5/3),""="",2^(2x))}}}

Next, write {{{8}}} as {{{2^3}}}

{{{matrix(2,3, "","","",
             (2^3)^(5/3),""="",2^(2x))}}}

Next, we multiply the exponents of 2 on the left {{{3*expr(5/3)}}} getting 5

{{{matrix(1,3,2^5,""="",2^(2x) )}}}

Now that the bases are the same on both sides and they are 2, 
which is positive and not 1, we merely equate the exponents
of 2:

{{{matrix(1,3,5,""="",2x)}}}

{{{matrix(1,3,5/2,""="",x)}}}

Edwin</pre>