Question 24595
{{{(x^2)^(1/3) = 4}}} 
cube both sides (raise each side to the 3 power
{{{((x^2)^(1/3))^3 = 4^3}}}
take it slow - do every step
when you cube something, you multiply it by itself 3 times
{{{((x^2)^(1/3))((x^2)^(1/3))((x^2)^(1/3)) = 4^3}}}
the rule is you add the exponents when you have something like
{{{2^2 * 2^2 * 2^2 = 2^(2 + 2 + 2) = 2^6 = 64}}}
so you've got
{{{(x^2)^(1/3 + 1/3 + 1/3) = 4^3}}}
{{{(x^2)^1 = 4^3}}}
something raised to the 1 power is just the thing itself
take the square root of both sides
{{{x = (4^3)^(1/2)}}}
{{{x = 64^(1/2)}}}
{{{x = 8}}}