Đáp án: $-\dfrac1{36}$
Giải thích các bước giải:
Ta có:
$\dfrac{7\cdot 4^{13}\cdot 9^8-8^9\cdot 4\cdot 3^{10}\cdot 9^3}{5\cdot 6^{19}\cdot 2^9-27^6\cdot 7\cdot 16\cdot 2^{25}}$
$=\dfrac{7\cdot (2^2)^{13}\cdot (3^2)^8-(2^3)^9\cdot 2^2\cdot 3^{10}\cdot (3^2)^3}{5\cdot (2\cdot 3)^{19}\cdot 2^9-(3^3)^6\cdot 7\cdot 2^4\cdot 2^{25}}$
$=\dfrac{7\cdot 2^{26}\cdot 3^{16}-2^{27}\cdot 2^2\cdot 3^{10}\cdot 3^6}{5\cdot 2^{19}\cdot 3^{19}\cdot 2^9-3^{18}\cdot 7\cdot 2^4\cdot 2^{25}}$
$=\dfrac{7\cdot 2^{26}\cdot 3^{16}-2^{29}\cdot 3^{16}}{5\cdot 2^{28}\cdot 3^{19}-3^{18}\cdot 7\cdot 2^{29}}$
$=\dfrac{2^{26}\cdot 3^{16}\cdot (7-2^{3})}{2^{28}\cdot 3^{18}(5\cdot 3-7\cdot 2)}$
$=\dfrac{2^{26}\cdot 3^{16}\cdot (7-8)}{2^{28}\cdot 3^{18}(15-14)}$
$=\dfrac{2^{26}\cdot 3^{16}\cdot (-1)}{2^{28}\cdot 3^{18}\cdot 1}$
$=-\dfrac{2^{26}\cdot 3^{16}}{2^{28}\cdot 3^{18}}$
$=-\dfrac{1}{2^{2}\cdot 3^{2}}$
$=-\dfrac1{36}$
