A rectangle has the length of \sqrt[3]{81} and a width of 3 (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 …

Question

A rectangle has the length of


`\sqrt[3]{81}`
and a width of

`3 (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

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

Explanation:

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