Question 198436
When you see an expression such as {{{x^(2/3)}}}, it means that you must square the x (that's the what the 2 in the numerator of the exponent means) squared then you take the cube root of the result (that's what the 3 in the denominator indicates).
Now if you see {{{x^(2/3) = 25}}} you can find x by raising both sides to the power that's the inverse of the given exponent {{{2/3}}}, like this:
{{{(x^(2/3))^(3/2) = (50)^(3/2)}}} On the left side, you have to multiply the exponents to get an exponent of 1 {{{(x^(2/3))^(3/2) = x^((2/3)*(3/2))}}}={{{x^1 = x}}}
So now you have:
{{{x = 25^(3/2)}}} So you now cube the 25 {{{25^3 = 15625}}} and then take the square root of 15625 {{{sqrt(15625) = 125}}} and so...
{{{x = 125}}}
Now let's look at your problem:

{{{2(x-2)^(2/3) = 50}}} Divide both sides by 2.
{{{(x-2)^(2/3) = 25}}} Now raise both sides to the power {{{3/2}}}
{{{((x-2)^(2/3))^(3/2) = (25)^(3/2)}}} Multiply the exponents on the left side.
{{{(x-2) = sqrt(25^3)}}}
{{{x-2 = sqrt(15625)}}}
{{{x-2 = 125}}} Add  2 to both sides.
{{{highlight(x = 127)}}}