Complete the proof. Given: AB∙BP=CB∙BM
Prove: ∆CBA~∆PBM

Statements
Reasons
AB∙BP=CB∙BM
5.
ABCB=??
6. Property of ?
∠CBA≅∠???
7.
∆CBA~∆PBM
8.

A does not. You are getting something like 15^9/5, as an example, which is very much larger than 3^9. So A is wrong.

B is correct. (15/5)^x = 3^x Both 15 and 5 are inside the brackets.

C is correct. 3^1 * 3^(x - 1) = 3^(x - 1 + 1) = 3^x

D is correct (15^x)/5^x = (15/5)^x = 3^x

E is not correct. It is not a general case and the base number is 3 not x.

F is not correct. 3^1*3^(x + 1) = 3^(x + 2) not correct.

B C and D are correct. The rest are not.