The purple shape is a dilation of the black shape. What is the scale factor of the dilation?

Im literally having a mental breakdown

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.

How many times larger is 6 × 10^12 than 2 × 10^7? a. 30,000 b. 3,000 c. 3,000,000 d. 300,000