Question 169922
{{{3*root(3,64x)+3*root(3,27x)}}} Start with the given expression



{{{3*root(3,4^3x)+3*root(3,3^3x)}}} Rewrite {{{64}}} as {{{4^3}}}. Rewrite {{{27}}} as {{{3^3}}}



{{{3*root(3,4^3)*root(3,x)+3*root(3,3^3)*root(3,x)}}} Break up the roots. Note: {{{root(3,4^3x)=root(3,4^3)*root(3,x)}}}



{{{3*4*root(3,x)+3*3*root(3,x)}}} Take the cube root of {{{4^3}}} to get 4. Take the cube root of {{{3^3}}} to get 3



{{{12*root(3,x)+9*root(3,x)}}} Multiply



Let {{{z=root(3,x)}}}



{{{12z+9z}}} Replace {{{root(3,x)}}} with "z"



{{{21z}}} Combine like terms.



{{{21*root(3,x)}}} Plug in {{{z=root(3,x)}}}



So {{{3*root(3,64x)+3*root(3,27x)=21*root(3,x)}}}