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