Đáp án + Giải thích các bước giải:
Ta có :
`\frac{3^{15}.2^{22}+6^{16}.4^{4}}{2.9^{9}.8^{7}-27^{5}.2^{23}}`
`=\frac{3^{15}.2^{22}+2^{16}.3^{16}.(2^{2})^{4}}{2.(3^{2})^{9}.(2^{3})^{7}-(3^{3})^{5}.2^{23}}`
`=\frac{3^{15}.2^{22}+2^{16}.3^{16}.2^{2.4}}{2.3^{2.9}.2^{3.7}-3^{3.5}.2^{23}}`
`=\frac{3^{15}.2^{22}+2^{16}.3^{16}.2^{8}}{2.3^{18}.2^{21}-3^{15}.2^{23}}`
`=\frac{3^{15}.2^{22}+2^{24}.3^{16}}{2^{22}.3^{18}-3^{15}.2^{23}}`
`=\frac{3^{15}.2^{22}(1+2^{2}.3)}{2^{22}.3^{15}(3^{3}-2)}`
`=\frac{1+2^{2}.3}{3^{3}-2}`
`=\frac{13}{25}`
Vậy `\frac{3^{15}.2^{22}+6^{16}.4^{4}}{2.9^{9}.8^{7}-27^{5}.2^{23}}=\frac{13}{25}`
