Question

​​​\(\dfrac{27^{10}+9^5}{9^{13}+27^2}\)​

Answer 1

\(\dfrac{27^{10}+9^5}{9^{13}+27^2}=\dfrac{\left(3^3\right)^{10}+\left(3^2\right)^5}{\left(3^2\right)^{13}+\left(3^3\right)^2}\)  = \(\dfrac{3^{30}+3^{10}}{3^{26}+3^6}=\dfrac{3^{10}\left(1+3^{20}\right)}{3^6\left(1+3^{20}\right)}=3^4=81\)

Answer 2

\(=\dfrac{3^{30}+3^{10}}{3^{26}+3^6}=\dfrac{3^{10}\left(3^{20}+1\right)}{3^6\left(3^{20}+1\right)}=3^4=81\)