\(\frac{4^5.9^4-2.6^9}{2^{10}.3^8+6^8.20}\)
\(=\frac{\left(2^2\right)^5.\left(3^3\right)^4-2.\left(2.3\right)^9}{2^{10}.3^8+\left(2.3\right)^8.2.10}\)
\(=\frac{2^{10}.\left(3^{12}-3^9\right)}{2^{10}.3^8.\left(1+5\right)}\)
\(=\frac{3^9\left(3^3-1\right)}{3^8.3.2}\)
\(=\frac{3^9.26}{3^9.2}\)
\(=\frac{26}{2}=13\)
\(\frac{4^5\times9^4-2\times6^9}{2^{10}\times3^8+6^8\times20}=\frac{\left(2^2\right)^5\times\left(3^2\right)^4-2\times6\times6^8}{2^2\times2^8\times3^8+6^8\times20}=\frac{2^{10}\times3^8-12\times6^8}{2^2\times\left(2\times3\right)^8+6^8\times20}\)
\(=\frac{2^2\times2^8\times3^8-12\times6^8}{4\times6^8+6^8\times20}=\frac{2^2\times\left(2\times3\right)^8-12\times6^8}{6^8\times\left(4+20\right)}=\frac{4\times6^8-12\times6^8}{6^8\times24}=\frac{6^8\times\left(4-12\right)}{6^8\times24}=\frac{-8}{24}=-\frac{1}{3}\)
\(4^5.9^4-2.6^9\)
=\(\left(2^2\right)^5.\left(3^2\right)^4-2.\left(2.3\right)^9\)
=\(2^{10}.3^8-2.2^9.3^9\)
=\(2^{10}.3^8-2^{10}.3^9\)
=\(3^8-3^9\)
=-13122
