Question

The sides of a square are two to the power of four-ninths inches long. What is the area of the square?

two to the power of the fraction sixteen over eighty-one square inches
four to the power of the fraction sixteen over eighty-one square inches
two to the power of eight-ninths square inches
four to the power of eight-ninths square inches

Answer 1

2^(8/9) in²

Explanation:

Make use of the identity ...

... (a^b)^c = a^(bc)

Here, you have a=2, b=4/9, c=2. There is an additional factor (units of inches) inside the parentheses on the left. For that, you use the identity

... (ab)^c = a^c·b^c

In this case a = 2^(4/9), b = in, c = 2.

So, the working of your problem is ...

... Area = (side length)^2 = (2^(4/9) in)^2 = (2^(4/9))^2 in^2

... = 2^(4/9·2) in^2 = 2^(8/9) in^2