Question

Tính: \(\left(2^{19}.27^3+15.4^9.9^4\right):\left(6^9.2^{10}+12^{10}\right)\)

Help me !!!

Answer 1

\(\left(2^{19}.27^3+15.4^9.9^4\right):\left(6^9.2^{10}+12^{10}\right)\)

\(=\left[2^{19}.\left(3^3\right)^3+3.5.\left(2^2\right)^9.\left(3^2\right)^4\right]:\left[2^9.3^9.2^{10}+2^{10}.6^{10}\right]\)

\(=\left(2^{19}.3^9+3.5.2^{18}.3^8\right):\left(2^{19}.3^9+2^{10}.2^{10}.3^{10}\right)\)

\(=\left(2^{19}.3^9+5.3^9.2^{18}\right):\left(2^{19}.3^9+2^{20}.3^{10}\right)\)

\(=2^{18}.3^9.\left(1.2+5\right):2^{19}.3^9.\left(1+2.3\right)\)

\(=\left(2^{18}.3^9.7\right):\left(2^{18}.2.3^9.7\right)\)

\(=1:2\)

\(=0.5\)