Tìm n biết:

\(\dfrac{{{8^7} + {8^7} + {8^7} + {8^7}}}{{{3^7} + {3^7}+ {3^7}}}:\dfrac{{{2^7} + {2^7}}}{{{6^7} + {6^7} + {6^7} + {6^7} + {6^7} + {6^7}}} = {2^n}\)

\(\begin{array}{l}\dfrac{{{8^7} + {8^7} + {8^7} + {8^7}}}{{{3^7} + {3^7} + {3^7}}}:\dfrac{{{2^7} + {2^7}}}{{{6^7} + {6^7} + {6^7} + {6^7} + {6^7} + {6^7}}} = {2^n}\\ \Leftrightarrow \dfrac{{{{4.8}^7}}}{{{{3.3}^7}}}:\dfrac{{{{2.2}^7}}}{{{{6.6}^7}}} = {2^n}\\ \Leftrightarrow \dfrac{{{{4.8}^7}}}{{{3^8}}}:\dfrac{{{2^8}}}{{{6^8}}} = {2^n}\\ \Leftrightarrow \dfrac{{{{4.8}^7}}}{{{3^8}}}.\dfrac{{{6^8}}}{{{2^8}}} = {2^n}\\ \Leftrightarrow \dfrac{{{2^2}.{{({2^3})}^7}{{.6}^8}}}{{{{(3.2)}^8}}} = {2^n}\\ \Leftrightarrow \dfrac{{{2^2}{{.2}^{21}}{{.6}^8}}}{{{6^8}}} = {2^n}\\ \Leftrightarrow {2^{23}} = {2^n}\\ \Leftrightarrow 23 = n\end{array}\)

Vậy n = 23