Cracking The SAT Premium

within  them.   For example,

(3x)^2  =   9x^2 ,  not 3x^2.

Similarly,   ,  not

. But the distribution rule
applies only when you
multiply or divide. (x + y)^2 =
x^2 + 2xy + y^2 , not x^2 + y^2.

MADSPM

To remember the exponent rules, all you need to do is remember the acronym MADSPM. Here’s what it
stands for:

• Multiply → Add


• Divide → Subtract


• Power → Multiply

Whenever you see an exponent problem, you should think MADSPM. The three MADSPM rules are the
only rules that apply to exponents.

Here’s a typical SAT exponent problem:

14.For  the equations       =   a^10    and (ay)^3  =   ax, if  a   >   1,  what    is  the value   of  x   ?

A) 5

B) 10

C) 15

D) 20

Here’s How to Crack It

This problem looks pretty intimidating with all those variables. In fact, you might be about to cry
“POOD” and go on to the next problem. That might not be a bad idea but before you skip the question,
pull out those MADSPM rules.

For the first equation, you can use the Divide-Subtract rule: = ax–y = a^10 . In other words, the first

equation tells you that x − y = 10.

For the second equation, you can use the Power-Multiply rule: (ay)^3 = a^3 y = ax. So, that means that 3y = x.

Now, it’s time to substitute: x − y = 3y − y = 10. So, 2y = 10 and y = 5. Be careful, though! Don’t choose
(A). That’s the value of y, but the question wants to know the value of x. Since x = 3y, x = 3(5) = 15,
which is (C).