CHAPTER 5 REVIEW
You should be able to do the following:
I
Simplify expressions with exponents.
A. The rules of exponents that you must know are:
a. x a  x b  x a b
b
b. x a   x a b
x  x a
c.    a
y  y
xa
 x ab
d.
b
x
e. x 0  1 for x ≠ 0
a



B. A negative on an exponent means to take the reciprocal. For example, x 3 means 13 and

x
 1 means x 2 . In practice, a negative exponent moves a factor from the numerator to the
2
x
denominator or from the denominator to the numerator.




x 2 y 3 2
C. When simplifying an expression involving exponents such as  4 2  , begin by simplifying
x y 
what is inside the parentheses by moving any factors with negative exponents and combing
y 5 2
any factors with the same base. This will give you  6  and you are ready to go onto the
x 

next step.
D. Once you have the simplest possible expression within the parentheses, move to your right.
 over. In the example above, that will give you
If the exponent is negative, flip the fraction
x 6 2
x12
 5  and you can now square everything giving you 10
y
y 
E. Be careful! A negative number is not the same as a negative integer. For example, 23 is
5x
x
1
, not 2 3 . And,
is not the same as  .
3
y
5y
2



Perform
operations (+, -, x, ÷) with polynomials.


A. To add or subtract polynomials, you combine like terms. These are terms whose variable
factors are exactly the same. When subtracting, be sure to subtract every term of the
polynomial by changing all of the signs of the second polynomial. For example,
II

7x

2


 3xy  y 2  4x 2  6xy  y 2 = 7x 2  3xy  y 2  4 x 2  6xy  y 2

B. When multiplying two monomials, you can commute the factors and combine them. For
example,
x 3 y 2 3x 2 y 4 = 3 x 3 x 2 y 2 y 4 = 3x 5 y 6
 
     
C. When multiplying two binomials, use the FOIL (first-outer-inner-last) method. For example,
= 2x 2  7x 15
 2x 2 10x  3x 15
 (2x  3)(x  5)
D. When multiplying a binomial times a polynomial, you can either distribute horizontally or
use the vertical multiplication method.
The only advantage to doing it vertically is that it


automatically lines up like terms so you can add them.
E. When dividing a polynomial by a monomial, you should take each term of the polynomial
and write it as a fraction with the monomial as the denominator. Then, reduce each fraction.
For example:
6x 5 3x 4 9x 2
2
2
5
4
2
2
6x  3x  9x  2 3x  = 3x 2  3x 2  3x 2  3x 2 =  2x 3  x 2  3  3x 2
F. When dividing a polynomial by a binomial, you must do long division. The most likely
place to make a mistake is when you are subtracting. Remember to subtract both terms!



III
Write terms in scientific notation and do calculations in scientific notation.
A. A number written in scientific notation will have one digit to the left of the decimal point and
will be multiplied by a power of 10 equal to the number of places the decimal point moved.
If the original number is larger, the exponent will be positive. If the original number is
smaller, the exponent will be negative.
234.67  2.3467 10 2
and
0.0432  4.32 102
B. Some calculations can be made easier by first writing the numbers in scientific notation. For
example:


32000  0.0025
150  0.00012
You can simplify this fraction by combining the factors of 10 and reducing the numerical
factors in the numerator and denominator.

=

8  5 10 3 40 10 3 40000
3.2 10 4  2.5 103


=
3 3
9
9
1.5 10 2 1.2 104
