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.

Answer 1

The answer is  9 inches squared.

Answer 2

The area is 9 inches squared

Explanation:

The area of a rectangle is the multiplication of the lenght and the width

Let A be the area, L the lenght and W the width

A = LW

The given lenght is
`\sqrt[3]{81}` inches and the given width is
`3^{((2)/(3))}` inches

But using a property of exponentials you can rewrite the width as:

`(3^(2)) ^{(1)/(3) }`

There is another property of exponentials which says that:
`n^{(1)/(k) } = \sqrt[k]{n}`

So, the width can be written as:
`\sqrt[3]{3^(2) }`

Calculating the area:

`A=\sqrt[3]{81}(\sqrt[3]{9})`

The multiplication of two cube roots is the cube root of the multiplication of the two numbers

Therefore:

`A=\sqrt[3]{(81)(9)} = \sqrt[3]{729}`

A = 9
`(inches)^(2)`