If calculator use was allowed on this one, you could also do this question by plugging in the answer
choices, or PITA, which will be discussed in more detail later in this book. Of course, you still need to
know the MADSPM rules to do the question that way.
The Peculiar Behavior of Exponents
Raising a number to a power can have quite peculiar and unexpected results, depending on what sort of
number you start out with. Here are some examples.
- If you square or cube a number greater than 1, it becomes larger. For example, 2^3 = 8.
- If you square or cube a positive fraction smaller than one, it becomes smaller.
For example, = .- A negative number raised to an even power becomes positive. For example, (–2)^2 = 4.
- A negative number raised to an odd power remains negative. For example, (–2)^3 = –8.
You should also have a feel for relative sizes of exponential numbers without calculating them. For
example, 2^10 is much larger than 10^2 . (2^10 = 1,024; 10^2 = 100.) To take another example, 2^5 is twice as
large as 2^4 , even though 5 seems only a bit larger than 4.
See the Trap
The test writers may hope
you won’t know these
strange facts about
exponents and throw them
in as trap answers. Know-
ing the peculiar behavior
of exponents will help you
avoid these tricky pitfalls
in a question.Square Roots
The radical sign (√) indicates the square root of a number. For example, = 5. Note that square roots
cannot be negative. If the test writers want you to think about a negative solution, they’ll say x^2 = 25
because then x = 5 or x = –5.
The Only Rules You Need to Know
Here are the only rules regarding square roots that you need to know for the SAT:
- = . For example, = .