Up Your Score (40 page)

15
x
− 16
x
+ 48 = 33

Then solve for
x
.

x
= 15

Now you can solve for
y
. We don’t want to bore you to death, so trust us, it turns out to be –8.

If you have a graphing calculator, then just plug the equations in to get your answer.

The rules of exponents are pretty simple. Know them like the back of your hand.

1.
c
^a
×
c
^b
=
c
^a+b

3. (
c
^a
)
^b
=
c
^a×b

4.
c
^a
×
d
^a
= (
cd
)
^a

1. If the cube root of the square root of a number is 3, what is the number?

(A) 27

(B) 54

(C) 243

(D) 729

(E) 2187

First of all, figure out what they’re really asking. Make the unknown number
x
. So, they’re saying, if
x
is square-rooted and then cube-rooted, the answer is 3. What’s
x
?

In mathematical terms, then, it’s
. Since that looks too complicated, try to make it simpler:

And (D) is the right answer.

You could have also used the four exponent rules to know that
is really equal to
, and get the answer by taking 3 to the 6th power.

Are you shuddering? Don’t. Negative and fractional exponents look annoyingly complicated, but they’re not.

All you have to do for negative exponents to make sense is to make them into a fraction with 1 on top and the exponented number on the bottom (eliminating the negative, of course).

So:

Example 1: 2
x
^–2
= ?
You should immediately flip it upside down:

Fractional exponents are even easier, but it gets really stupid when we explain it with words. Just remember this:

A tip: If it looks scary, it probably isn’t. Just relax and rely on the tricks you’ve learned. You’ll be fine. So don’t panic!

So remember, a fractional exponent is just

Example 2: 4
^⅔
= ?
First, you should raise
x
to the
p
power, and
then take the
q
root: