Putting It All Together: Finding a Common Base
Knowing the preceding rules is essential for success on exponent questions, but
the GRE will make such questions difficult by forcing you to evaluate expressions
where it seems that none of these rules apply. To get past these difficulties, you
should always be concerned with manipulating what’s given to you to get to the
same base. By doing so, you can then use the rules that were just covered. Look at
the following:(8^4 )(32^5 ) =
A 29
B 220
C 237
D 820
E 25620To simplify the expression, rewrite the exponential terms to have the same
base. By doing so, you will be able to use the exponent rule that says you can
add the exponents when multiplying exponential terms with the same base:
8 = 2^3 , so 8^4 = (2^3 )^4. Using your exponent rules, you know this comes
out to 2^12.
32 = 2^5 , so 32^5 = (2^5 )^5. Using your exponent rules, you know this comes
out to 2^25.
Now you can use your rules! The expression now reads: (2^12 )(2^25 ). Since you
are multiplying exponential terms with the same base, you keep the base and
add the exponents: (2^12 )(2^25 ) = 2(12+25) = 2^37. The correct answer is C.
Let’s look at another example:
(8^6 )(9^3 )
66 =
A 7212
B 123
C 212
D 92
E 123Again, your focus should be to manipulate the numerator and denominator
so that all the terms are in their prime forms.
86 = (2^3 )^6 = 2^18
93 = (3^2 )^3 = 3^6
66 = (3 × 2)^6 = 3^6 × 2^6
So your new fraction is:
(2^18 )(3^6 )
(2^6 )(3^6 )272 PART 4 ■ MATH REVIEW03-GRE-Test-2018_173-312.indd 272 12/05/17 11:54 am