Question

a rectangle has the length of
$\sqrt[3]{81}$
and a width of
$3 \frac{2}{3}$
A. inches. find the area of each rectangle.
3^2/3 inches squared
B. 3^8/3 inches squared
C. 9 inches squared
D. 9^2/3 inches squared
​

Answer 1

Answer:

$\large\boxed{C.\ 9\ inches\ squared}$

Step-by-step explanation:

$\text{Use}\\\\a^\frac{m}{n}=\sqrt[n]{a^m}\\\\a^n\cdot a^m=a^{n+m}\\-----------------\\\\length=\sqrt[3]{81}=\sqrt[3]{3^4}=3^\frac{4}{3}\\\\width=3^\frac{2}{3}\\\\\text{The area of a rectangle:}\ A=width\cdot length.\\\text{Substitute:}\\\\A=3^\frac{4}{3}\cdot3^\frac{2}{3}=3^{\frac{4}{3}+\frac{2}{3}}=3^{\frac{4+2}{3}}=3^\frac{6}{3}=3^2=9$