Cracking The SAT Premium

x–n =   

• Fractional exponents are a fancy way of taking roots and powers:

    =   

Here’s an example:

14.If   x   >   0,  which   of  the following   is  equivalent  to  ?

I.

II.

III.

A) None

B) I    and II  only

C) II   and III only

D) I,   II, and III

Here’s How to Crack It

This problem really tests your knowledge of exponents. First, convert into an exponent, since all of

the Roman numerals contain expressions with exponents. (Plus, exponents are easier to work with

because they have those nice MADSPM rules.) So, using the definition of a fractional exponent, =

. You want the items in the Roman numerals to equal .

Now, it’s time to start working with the Roman numerals. In (I), the test writers are trying to be tricky.

(There’s a surprise.) There’s no exponent rule for adding exponent expressions with like bases. So, x +

    does    not equal    .  (If you want    to  be  sure,   you could   try a   number  for x:  If  x   =   4,  then        =   8,  but 4   +   

    =   4   +   2   =   6.) So, cross   off any answer  that    includes    (I):    (B) and (D) are gone.

Now, since you are down to either (A) or (C), all you really need to do is try either (II) or (III). If either