Question 4952
{{{x^(2/3)-9x^(1/3)+8}}}

Factor:
{{{(x^(1/3)-8)(x^(1/3)-1)}}}

Set it equal to zero:
{{{(x^(1/3)-8)(x^(1/3)-1)=0}}}
{{{x^(1/3)=8}}} or {{{x^(1/3)=1)}}}
cube both sides:
x=512 or x=1

check the solution with the original equation
{{{512^(2/3)-9(512)^(1/3)+8=0}}}
{{{64-72+8=0}}}
{{{1^(2/3)-9(1)^(1/3)+8=0}}}
{{{1-9+8=0}}}

Both of these are correct.