Question 286501
{{{ root(3,54c^4) }}} Start with the given expression.



{{{ root(3,2*27*c^3*c) }}} Factor 54 into 2*27 (note how 27 is a perfect cube) and factor {{{c^4}}} into {{{c^3*c}}}



{{{ root(3,2)*root(3,27)*root(3,c^3)*root(3,c) }}} Break up the root.



{{{ root(3,2)*3*c*root(3,c) }}} Take the cube root of 27 to get 3. Take the cube root of {{{c^3}}} to get {{{c}}}.



{{{ 3c*root(3,2c) }}} Rearrange the terms and combine the roots.



So {{{ root(3,54c^4) = 3c*root(3,2c) }}}