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

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.

Answer 2

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

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
`(2)/(3)`.

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

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

Therefore, the area of the rectangle is 9 inches squared