Question 190299
Is the expression {{{(27a^k - 9a^(k+2) + 15a^(k+4))/(3a^k)}}}???



{{{(27a^k - 9a^(k+2) + 15a^(k+4))/(3a^k)}}} Start with the given expression



{{{(27a^k - 9a^k*a^2 + 15a^k*a^4)/(3a^k)}}} Factor {{{a^(k+2)}}} into {{{a^k*a^2}}}. Factor {{{a^(k+4)}}} into {{{a^k*a^4}}}



Note: use the identity {{{x^(y+z)=x^y*x^z}}}



{{{(3a^k*(9 - 3a^2 + 5a^4))/(3a^k)}}} Factor out the GCF {{{3a^k}}} from the numerator



{{{(highlight(3a^k)(9 - 3a^2 + 5a^4))/(highlight(3a^k))}}} Highlight the common terms.



{{{(cross(3a^k)(9 - 3a^2 + 5a^4))/(cross(3a^k))}}} Cancel out the common terms.



{{{9 - 3a^2 + 5a^4}}} Simplify



{{{5a^4-3a^2+9}}} Rearrange the terms.



So {{{(27a^k - 9a^(k+2) + 15a^(k+4))/(3a^k)=5a^4-3a^2+9}}} where {{{a<>0}}}