Exponent Question in FoM

[burns.nelson]

FoM, Chapter 3, Exponents & Roots, Drill Sets, page 133 #7:

7. (3^2)^-3

Answer is 3^-6

This answer makes sense when considering the theory of (a^m)^n, which is a^mn. However, with integers, can the answer above also be 9^-3? Both 3^-6 and 9^-3 equal 1/729, so I'm confused by the PEMDAS order of options or just plain theory.

[RonPurewal]

9^-3 and 3^-6 are the same number, so there's no meaningful difference.

...unless the directions are more specific. for instance, if the directions specify that you should have (prime)^(integer) then you'd have to express it as 3^-6 (since 9 is not prime).

[RonPurewal]

by the way, this is the wrong folder for this thread, so it's now locked. if you have further questions about this item, please post in the Manhattan Prep non-CAT folder.

thank you.