Answer:
The area is 9 inches squared
Step-by-step 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 [tex]\sqrt[3]{81}[/tex] inches and the given width is [tex]3^{(\frac{2}{3})}[/tex] inches
But using a property of exponentials you can rewrite the width as:
[tex](3^{2}) ^{\frac{1}{3} }[/tex]
There is another property of exponentials which says that: [tex]n^{\frac{1}{k} } = \sqrt[k]{n}[/tex]
So, the width can be written as: [tex]\sqrt[3]{3^{2} }[/tex]
Calculating the area:
[tex]A=\sqrt[3]{81}(\sqrt[3]{9})[/tex]
The multiplication of two cube roots is the cube root of the multiplication of the two numbers
Therefore:
[tex]A=\sqrt[3]{(81)(9)} = \sqrt[3]{729}[/tex]
A = 9 [tex](inches)^{2}[/tex]
