Question

A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.

Select one:
a. 3 to the 2 over 3 power inches squared
b. 3 to the 8 over 3 power inches squared
c. 9 inches squared
d. 9 to the 2 over 3 power inches squared

Answer 1

`A=length *width \\ \\A= \sqrt[3]{81}*3^{ (2)/(3)} =\sqrt[3]{3^4}*3^{ (2)/(3)} =3^{ (4)/(3)}*3^{ (2)/(3)}=3^{ (4)/(3) + (2)/(3)}=3^{ (6)/(3)}=3^2=9 \ in^2`