Question

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2¹•3⁸
____
36³​

Answer 1

Решение и ответ:

$\displaystyle \frac{{{2^1} \cdot {3^8}}}{{{{36}^3}}} = \frac{{{2^1} \cdot {3^8}}}{{{{\left( {4 \cdot 9} \right)}^3}}}=\frac{{{2^1} \cdot {3^8}}}{{{{\left( {{2^2}} \right)}^3} \cdot {{\left( {{3^2}} \right)}^3}}}=\frac{{{2^1} \cdot {3^8}}}{{{2^{2 \cdot 3}} \cdot {3^{2 \cdot 3}}}} = \frac{{{2^1} \cdot {3^8}}}{{{2^6} \cdot {3^6}}}={2^{1-6}} \cdot {3^{8-6}}={2^{-5}} \cdot {3^2} = \frac{{{3^2}}}{{{2^5}}} = \frac{9}{{32}}$