Answer:
9 square inches.
Step-by-step explanation:
We have been given that a rectangle has a length of the [tex]\sqrt[3]{81}[/tex] inches and a width of [tex]3^{\frac{2}{3}}[/tex] power inches. We are asked to find the area of given rectangle.
We know that area of rectangle in length times width of rectangle.
[tex]\text{Area of rectangle}=\sqrt[3]{81}\times 3^{\frac{2}{3}}[/tex]
We can write 81 as [tex]3^4[/tex] as:
[tex]\text{Area of rectangle}=\sqrt[3]{3^4}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex], we can write [tex]\sqrt[3]{3^4}=3^{\frac{4}{3}}[/tex].
[tex]\text{Area of rectangle}=3^{\frac{4}{3}}\times 3^{\frac{2}{3}}[/tex]
Using exponent rule [tex]a^b\cdot a^c=a^{b+c}[/tex], we will get:
[tex]\text{Area of rectangle}=3^{\frac{4}{3}+\frac{2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{4+2}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{\frac{6}{3}}[/tex]
[tex]\text{Area of rectangle}=3^{2}[/tex]
[tex]\text{Area of rectangle}=9[/tex]
Therefore, the area of given rectangle is 9 square inches.
