Question 355697
formula is:


8x^3 - 1 = 0


add 3 to both sides of the equation to get:


8x^3 = 1


divide both sides of the equation by 8 to get:


x^3 = (1/8)


Take the cube root of both sides of the equation to get:


x = (1/8)^(1/3) which looks like {{{x = (1/8)^(1/3) }}}


this can also be written as x = root(3,(1/8)) which looks like {{{ root(3,(1/8)) }}}


you can use your calculator to solve this to get x = (1/2).


you can also see that {{{ root(3,(1/8)) }}} is the same as {{{root(3,(1/2)*(1/2)*(1/2))}}} which is the same as {{{root(3,(1/2)^3)}}}


You should also be able to see that {{{root(3,(1/2)^3)}}} is the same as {{{((1/2)^3)^(1/3)}}} which is the same as {{{(1/2)^(3*(1/3))}}} which becomes {{{(1/2)^1}}} which becomes {{{(1/2)}}}.