It is known that the a power of 3 times the b power of 5 = the c power of 3 times the d power of 5 = 1.

Then: the d power of (a power of 3 times b power of 5) = the b power of (c power of 3 times d power of 5) = 1.

That is: ad power of 3 * bd power of 5 = bc power of 3 * bd power of 5.

Because the bd power of 5 >: 0

So: the ad power of 3 = the bc power of 3.

So: ad=bc