Answer:
[tex]\large\boxed{C.\ 9\ inches\ squared}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\a^\frac{m}{n}=\sqrt[n]{a^m}\\\\a^n\cdot a^m=a^{n+m}\\-----------------\\\\length=\sqrt[3]{81}=\sqrt[3]{3^4}=3^\frac{4}{3}\\\\width=3^\frac{2}{3}\\\\\text{The area of a rectangle:}\ A=width\cdot length.\\\text{Substitute:}\\\\A=3^\frac{4}{3}\cdot3^\frac{2}{3}=3^{\frac{4}{3}+\frac{2}{3}}=3^{\frac{4+2}{3}}=3^\frac{6}{3}=3^2=9[/tex]
