Question 126524
{{{root(3,a)(root(3,3a^2)+root(3,81a^2))}}} Start with the given expression




{{{root(3,a)*root(3,3a^2)+root(3,a)*root(3,81a^2)}}} Distribute



{{{root(3,(a)*(3a^2))+root(3,(a)*(81a^2))}}} Combine the roots



{{{root(3,3a^3)+root(3,81a^3)}}} Multiply



{{{a*root(3,3)+3a*root(3,3)}}} Simplify {{{root(3,3a^3)}}} to get {{{a*root(3,3)}}}. Simplify {{{root(3,81a^3)}}} to get {{{3a*root(3,3)}}}.



{{{root(3,3)(a+3a)}}} Factor out the GCF {{{root(3,3)}}}



{{{root(3,3)(4a)}}} Combine like terms



{{{4a*root(3,3)}}} Rearrange the terms





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Answer:



So {{{root(3,a)(root(3,3a^2)+root(3,81a^2))}}} simplifies to {{{4a*root(3,3)}}}




In other words, {{{root(3,a)(root(3,3a^2)+root(3,81a^2))=4a*root(3,3)}}}