Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$3^{13}$
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: $=3^{9+4} \\=3^{13}$