Question 1105183
Third root of a^8 / (√a)^3 = a^x , where a > 1 
 In the equation above, what is the value of x? 
{{{(a^8/((sqrt(a))^3))^(1/3)}}} = {{{a^x}}}
multiply the inside exponents by the outside exponent, 1/3 
{{{(a^(8/3)/((sqrt(a))^1))}}} = {{{a^x}}}; the top exponent is 8/3
the denominator can be written
{{{(a^(8/3)/a^(1/2))}}} = {{{a^x}}}
:
{{{a^(8/3-1/2)}}} = {{{a^x}}}; that's {{{8/3-1/2}}}
{{{a^(16/6-3/6)}}} = {{{a^x}}}, that's {{{16/6-3/6}}}
{{{a^(13/6)}}} = {{{a^x}}}, that's {{{13/6}}}
therefore
x = {{{13/6}}}