The next step is to look for factors common to the numerator and
denominator. The 6 on top and the 8 on bottom reduce to 3 over 4—so it
already looks like the answer’s going to be (D) or (E). The x^2 on top cancels
with the x^6 on bottom, leaving x^4 on bottom. You’re actually subtracting the
exponents: 2 – 6 = –4, since x–4 is the same as The y^12 on top cancels with
the y^3 on bottom, leaving y^9 on top. And the z^6 on top cancels with the z^3 on
bottom, leaving z^3 on top:
The answer is (E).
ADDING, SUBTRACTING, AND MULTIPLYING
POLYNOMIALS
Algebra is the basic language of the Mathematics Subject Tests, and you will
want to be fluent in that language. You might not get a whole lot of questions
that ask explicitly about such basic algebra procedures as combining like
terms, multiplying binomials, or factoring algebraic expressions, but you will
do all of those things in the course of working out the answers to more
advanced questions. So it’s essential that you be at ease with the mechanics
of algebraic manipulations.