Answer
$3^{13}$
Work Step by Step
Convert/write each base to base 3 to obtain:
$81^{3} \div 27 \cdot 9^2
\\=(3^4)^{3} \div 3^3 \cdot (3^2)^2$
Use the power rule ($(a^m)^n=a^{mn}$) to obtain:
$=3^{4(3)} \div 3^3 \cdot 3^{2(2)}
\\=3^{12} \div 3^3 \cdot 3^4$
Use the rule $a^m \div a^n = a^{m-n}$ to obtain:
$=3^{12-3} \cdot 3^4
\\=3^{9} \cdot 3^4$
Use the rule $a^m \cdot a^n = a^{m+n}$ to obtain:
$=3^{9+4}
\\=3^{13}$
