M Prep F of Math pp 104 Exponent Question 75^3*45^3/15^8

[mkofron]

75^3*45^3/15^8

The answer is 15.

Why can't you just reduce everything by 15 and go from there? I tried this an it didn't work. I just want to know why I can't do this.

Thank you for the help.

[melguy]

75³ x 45³
---------
15^8

75³ x 45³
-----------------
15³ x 15³ x 15² (I have broken it down just to show you easier division)

Solve and you get

15³
---- = 15
15²

P.S. You can multiply and divide same powers e.g. 3³ x 15³ = (3 x 15)³.
Incorrect 3² x 15³ = (3 x 15)²+³

[[email protected]]

Hi mkofron,

When dealing with complex-looking calculations, it sometimes helps to create a much-simpler example, so that you can be clear on how the rules of math apply.

Consider this simple example:

(4)(8)/2

What does the above fraction equal? It doesn't take much work to calculate it:

(4)(8)/2 = 32/2 = 16

Now what would have happened if you just "reduced everything by 2?".... You would have ended up with 8, which is NOT correct. Thus, you cannot just 'reduce everything by 15" in this question.

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

You actually can!

75³ * 45³ / 15� =

15³ * 5³ * 15³ * 3³ / (15³ * 15³ * 15²) =

5³ * 3³ / 15² =

15