McGraw-Hill Education GRE 2019

Use your exponent rules for division and you get 2(18− 6) × 3^0. And this comes

out to 2^12. The correct answer is C.

Table 1 lists the major exponent rules. You should commit these rules

to memory and make sure that you understand the conceptual basis

behind these rules, as outlined in this chapter.

Table 1 Exponent Rules Table

Rule Example

ax^ × ay = ax + y

bx^ × ax = (ba)x

(ax )^ y = axy

ax

ay

=ax – y

bx

ax

b

a

x

=⎛⎜⎝ ⎞⎟⎠

32 × 52 = (3^ × 5)^2 = 15^2

(3^2 )^5 = 3^10

35

32

= 33

32 × 34 = 3^6

(^15252)
32
15
3
2
==⎛⎜⎝ ⎞⎟⎠
Table 2 lists common powers and roots that appear on the GRE. Committing these
rules to memory will help you save precious time on the exam.
Table 2 Common Powers & Roots
22 = 4
23 = 8
24 = 16
25 = 32
26 = 64
27 = 128
32 = 9
33 = 27
34 = 81
42 = 16
43 = 64
44 = 256
52 = 25
53 = 125
54 = 625
4 = 2√
9 = 3√
√16 = 4
√25 = 5
36 = 6√
49 = 7√
64 = 8√
81 = 9√
100 = 10√
√121 = 11
√144 = 12
√169 = 13
√400 = 20
625 = 25√
Solving for an Unknown Exponent
So far, most of the questions that you have looked at have concerned shortcuts for
evaluating exponential expressions. Sometimes, however, you will be asked to solve
for a variable that is in the place of an exponent. Look at the following example:
If 2x = 8, then what is the value of x?
CHAPTER 11 ■ ALGEBRA 273
03-GRE-Test-2018_173-312.indd 273 12/05/17 11:54 am