Question 148163
{{{(root(5,9)-root(5,81))/(root(5,3))}}} Start with the given expression.



{{{(root(5,9)-root(5,9*9))/(root(5,3))}}} Factor 81 into 9*9



{{{(root(5,9)-root(5,9)*root(5,9))/(root(5,3))}}} Break up the root.



{{{(root(5,9)(1-root(5,9)))/(root(5,3))}}} Factor out the GCF {{{root(5,9)}}}



{{{(root(5,3*3)(1-root(5,9)))/(root(5,3))}}} Factor 9 into 3*3



{{{(root(5,3)*root(5,3)(1-root(5,9)))/(root(5,3))}}} Break up the root.



{{{(highlight(root(5,3))*root(5,3)(1-root(5,9)))/(highlight(root(5,3)))}}} Highlight the common terms.



{{{(cross(root(5,3))*root(5,3)(1-root(5,9)))/(cross(root(5,3)))}}} Cancel out the common terms.



{{{root(5,3)(1-root(5,9))}}} Simplify



{{{root(5,3)*1-root(5,3)*root(5,9))}}} Distribute



{{{root(5,3)-root(5,27)}}} Combine the roots and multiply



So {{{(root(5,9)-root(5,81))/(root(5,3))}}} simplifies to {{{root(5,3)-root(5,27)}}}


In other words, {{{(root(5,9)-root(5,81))/(root(5,3))=root(5,3)-root(5,27)}}}