There’s nothing tricky about this question if you know how to work with exponents. The first step is
to eliminate the parentheses by distributing the square in the denominator:
The next step is to look for factors common to the numerator and denominator. The 4 on top and
the 4 on the bottom cancel each other out, so it already looks like the answer’s going to be (C) or (D).
The e^4 on top cancels with the e^6 on the bottom, leaving e^2 on bottom. You’re actually subtracting
the exponents: 4 − 6 = −2, since e−2 is the same as . The d 3 on top cancels with the d^2 on the
bottom, leaving d on top. And the f 2 on top and the f 2 on bottom cancel each other out.
The answer is (D).
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.
Combining like terms: To combine like terms, keep the variable part unchanged while adding or
subtracting the coefficients:
4. (xn)(yn) = (xy)n5.