How to write 6.7 different ways

Does the point (1, sqrt 7) lie on circle shown.

Adecorative window is made up of a rectangle with semicircles at either end. the ratio of ad to ab is 3: 2 and ab is 30 inches. what is the ratio of the area of the rectangle to the combined area of the semicircles? possible answers: a. 2: 3 b. 3: 2 c. 6: π d. 9: π e. 30: π

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.