Question 201790
your formula looks like this:
{{{(sqrt(x))^((1/3)) * ((sqrt(3*x^2))^((1/3)) - (sqrt (81*x^2))^((1/3)))}}} if I understand it correctly.
since {{{sqrt(x)}}} is the same as {{{x^(1/2)}}} this formula can be rewritten as follows:
{{{ (x^(1/2))^(1/3) * (((3*x^2)^(1/2))^(1/3) - ((81*x^2)^(1/2))^(1/3))}}}
since by the rules of exponents {{{(x^a)^b}}} is equal to {{{x^(a*b)}}}, this formula can be rewritten as follows:
{{{ x^(1/6) * ((3*x^2)^(1/6) - (81*x^2)^(1/6)))}}}
since {{{(a*b)^c}}} is equal to {{{a^c*b^c}}}, this formula can be rewritten as follows:
{{{x^(1/6)*((3^(1/6)*x^(1/3)) - (81^(1/6)*x^(1/3)))}}}
since {{{x^(1/3)}}} is a common factor, it can be factored out to get:
{{{x^(1/6)*x^(1/3)*(3^(1/6)-81^(1/6))}}}
which simplifies to:
{{{x^(1/2)*(3^(1/6)-81^(1/6))}}}
which i do not believe can be simplified any further, so I reduced the constants to get:
{{{-.879146868 * x^(1/2)}}}
to prove the answer is correct, then take any value of x and solve the original equation and then solve the reduced equation.  you should get the same answer.
I did it using a value of x = 4, 12, and 27.
You can use any value you wish if you want to take the time to prove it to yourself.