Foundations of GMAT Math - 4th ed/chap5/set 1/ drill 2/ Q5

[ally.uws]

The problem asks you to simplify:
[5^6 * 5^4x] / [5^4]
The answer is 5^(4x+2), which makes sense if you first add the numerator exponents together, then subtract the denominator's exponent. However, can't you also break down into:
[5^6 / 5^4] * [5^4x / 5^4]?
in this case, the answer appears to be 5^(4x-2), which would be different. can you explain what might be wrong with my approach via method 2?
many thanks,

[ninjasai]

The problem asks you to simplify:
[5^6 * 5^4x] / [5^4]
The answer is 5^(4x+2), which makes sense if you first add the numerator exponents together, then subtract the denominator's exponent. However, can't you also break down into:
[5^6 / 5^4] * [5^4x / 5^4]?
in this case, the answer appears to be 5^(4x-2), which would be different. can you explain what might be wrong with my approach via method 2?
many thanks,

Buddy... It doesn't work like that.

(a*b)/c cannot be equal to a/c *b/c
because a/c * b/c = (a*b)/c^2

Your rule applies to addition:
(a+b)/c = a/c + b/c

[ally.uws]

thank you!

[RonPurewal]

the post above contains a good explanation.