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.
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

Answer:

The correct answer is C. The area of the rectangle is 9 inches squared

Step-by-step explanation:

The formula for the area of a rectangle is A =L x W

where L is the length and W the width

we were given the length to be equal to $\sqrt[3]{81}$

this can be further simplified to $\sqrt[3]{9^{2} }$

The width was given to be 3$\frac{2}{3}$.

This can be further simplified using the law of indices to be $(3^{2}) \frac{1}{3}$ =$9^{\frac{1}{3} }$ =$\sqrt[3]{9}$

The area A = $\sqrt[3]{81}$ *$\sqrt[3]{9}$ = $(81*9)^{\frac{2}{3} }$  = $(\sqrt[3]{729})^{2}$ =$9^{2}$

Therefore, the area of the rectangle is 9 inches squared

Answer 2

Area of a rectangle is length times width:
3 to the (2 over 3) power is ∛3²
A=∛81*∛3²
A=3∛3 * ∛3²=3∛3³=3*3=9
the answer is C.