Your turn: using the figure, a
c
= d
a
.

what steps need to be taken to change this to a² = cd?

example: multiply by 2; divide by a, etc

To change a/x=d/a to a²=cd, you need to take the following steps:
 
 1. Pass the "a" to the left side and the "c" to the right side:
 
 (a)(a)/c=d
 (a)(a)=cd
 
 2. Finally, multiply "a" by "a": 
 
 a²=cd   (By definition, when you have to multiply exponents with the same base, you should add the exponents. As you can see, both bases "a" have exponents 1, so, when you multiply them, you have to rewrite the base and then add these exponents: a^1+1=a²).