می‌دانیم ${a^{ - n}} = {(\frac{1}{a})^n}$ و $\frac{{{a^n}}}{{{b^n}}} = {(\frac{a}{b})^n}$ و ${a^n} \times {a^m} = {a^{n + m}}$

${({a^n})^m} = {a^{n \times m}}$

$\frac{{{3^5} + {{(\frac{1}{3})}^{ - 3}} \times 9 + {{(\frac{1}{{27}})}^{ - 2}} \times \frac{1}{3}}}{{{5^{18}} \times \underbrace {{{(0/2)}^6}}_{{{(\frac{1}{5})}^6}}}} = \frac{{{3^5} + {3^3} \times 9 + {{(27)}^2} \times \frac{1}{3}}}{{{5^{18}} \times {5^{ - 6}} = {5^{18 - 6}} = {5^{12}}}} = \frac{{{3^5} + {3^3} \times {3^2} + ({3^{{3^2}}}) \times {3^{ - 1}}}}{{{5^{12}}}}$

$ = \frac{{{3^5} + {3^5} + {3^6} \times {3^{ - 1}}}}{{{5^{12}}}} = \frac{{{3^5} + {3^5} + {3^5}}}{{{5^{12}}}} = \frac{{3 \times {3^5}}}{{{5^{12}}}} = \frac{{{3^6}}}{{{{({5^2})}^6}}} = {(\frac{3}{{25}})^6}$