Here are the four steps to Problem Solving success:

Step 1: Get the Specs.

Step 2: Plan the Attack.

Step 3: Mine the Math.

Step 4: Power Through.

Let’s have a closer look.

Step 1: Get the Specs. Step 1 puts you in the right frame of mind to successfully work through a PS question. The main specifications that should interest you include the following:

Step 2: Plan the Attack. While knowing math concepts cold is necessary to succeed on GRE math, you still need to apply them effectively to solve the problems. In Step 2, you’ll determine how you’ll use what you know to answer the questions; that is, whether you’ll apply math concepts in a standard way and then search the choices for the answer you get, or whether it’s better to make up numbers or work backward. Use the information you discover as you scope out the problem in Step 1 to help you decide how to proceed.

Step 3: Mine the Math. With a solid plan in mind, you’ll then dig through your storehouse of Math 101 concepts to pick out the ones you’ll need to solve the problem. If the question concerns a right triangle, for example, then the Pythagorean theorem and rules for the length of the sides of right triangles should pop into your head. If you’re up against exponents, or an arithmetic mean situation, or a quadratic equation, then you’d pull concepts related to those topics from your reservoir of math knowledge. Don’t think you have to gather every single concept you’ll need at this stage; some necessary concepts will emerge as you proceed through the problem in Step 4. In Step 3, simply dig out the essential math concept or concepts you need to get started. Note that for easy reference, we’ve bolded all these math concepts whenever they appear in the explanations to our practice questions.

Step 4: Power Through. With relevant math concepts and a plan for how to use them firmly in mind, you’ll now be able to power through the question. “Power Through,” however, doesn’t necessarily imply using brute force, since in many cases clever or elegant solutions may be possible. How you do the work will depend on the method you choose in Step 2, and in many cases the standard approach works fine (hence, we call it “standard”). But in other cases you may settle on one of the alternative approaches we’ve shown you. Either way, Step 4 is the time to solve the problem and make your selection.

It’s time to test drive the method, so when you feel you have a good sense of the steps, sink your teeth into this:

Step 1: Get the Specs. The little raised 2s and 3s in the equation tell you you’re dealing with exponents, an arithmetic concept, and the huge powers that the as are raised to in the choices suggest it would be insane to try to make up numbers in this case.

Step 2: Plan the Attack. Nothing particularly fancy here—either you know the rules of exponents, or you don’t. (If you still don’t after our lengthy Math 101 chapter, back to chapter 2 for you!) Our analysis from Step 1 indicates that this problem is best approached via a standard application of the rules of exponents—precisely our concern in the next step.

Step 3: Mine the Math. The rule of negative exponents states that , something you need to know to deal with the a^–2 part of the expression. Beyond that, when multiplying terms with exponents containing the same base, we add the exponents, and something raised to a power and then taken to another power requires multiplying those exponents. These are the relevant math concepts you may need to call upon to simplify the expression.

Step 4: Power Through. Based on the concepts discussed above, . That means we can rewrite the expression as , and cancel out the a² from the top and bottom, leaving (a3)3. Multiplying the exponents gives us our final answer, a⁹, choice C.