Answer:
C. [tex]2\text{ Inches}^2[/tex]
Step-by-step explanation:
We have been given that length of rectangle is [tex]\sqrt[5]{16}[/tex] inches and width is [tex]2^{\frac{1}{5}}[/tex] inches. We are asked to find the area of the given rectangle.
[tex]\text{Area of rectangle}=\text{Length}\times \text{Width}[/tex]
Substitute given values:
[tex]\text{Area of rectangle}=\sqrt[5]{16}\text{ Inches}\times 2^{\frac{1}{5}}\text{ Inches}[/tex]
Writing 16 as [tex]2^4[/tex].
[tex]\text{Area of rectangle}=\sqrt[5]{2^4}\text{ Inches}\times 2^{\frac{1}{5}}\text{ Inches}[/tex]
Using property [tex]\sqrt[n]{a^m}=a^\frac{m}{n}}[/tex], we will get:
[tex]\text{Area of rectangle}=2^{\frac{4}{5}}\text{ Inches}\times 2^{\frac{1}{5}}\text{ Inches}[/tex]
[tex]\text{Area of rectangle}=2^{\frac{4}{5}}\times 2^{\frac{1}{5}}\text{ Inches}^2[/tex]
Using property [tex]a^m\times a^n=a^{m+n}[/tex], we will get:
[tex]\text{Area of rectangle}=2^{\frac{4}{5}+\frac{1}{5}}\text{ Inches}^2[/tex]
[tex]\text{Area of rectangle}=2^{\frac{4+1}{5}}\text{ Inches}^2[/tex]
[tex]\text{Area of rectangle}=2^{\frac{5}{5}}\text{ Inches}^2[/tex]
[tex]\text{Area of rectangle}=2^{1}\text{ Inches}^2[/tex]
[tex]\text{Area of rectangle}=2\text{ Inches}^2[/tex]
Therefore, the area of the given rectangle is 2 square inches and option C is the correct choices.
