Test 4 Review (Ch. 5) Math 102
Ch. 5: Exponents and polynomials.
5.1-2: Exponent “rules” and scientific notation.
1. You need to know what the “base” and “exponent” are for an exponential expression; for
example, in the expression
4
2
, 2 is the base and 4 is the exponent.
2. Know all the exponent rules we developed in class and be able to apply them meticulously to
the problems in the book (it is very easy to make mistakes or invent new rules!). I highly
encourage you to work at understanding why the rules are true. Understanding the logic behind
the rules makes them easier to remember and harder to use incorrectly. Also, when the
exponents are nice enough, you don’t even have to think about the formal rules as long as you
understand how to collect factors together. I’ve written a compact list below:
r s r s
a a a
+
=
( )
r
r r
ab a b
=
(
)
s
r rs
a a
=
(
)
s
r rs
a a
=
r
r
r
a a
b b
=
r
r s
s
a
a
a
−
= 0
1
a
=
1
r
r
a
a
−=
Note: we don’t consider an exponential expression to be “simplified” until there are no negative
exponents left in the expression.
3. Know how to put big and small numbers into scientific notation. Know how to take a number
in scientific notation and turn it back into “standard” form.
5.3: Operations with monomials.
1. A monomial is a product of constants and variables.
2. The only way you can add or subtract monomials is if the variable parts are exactly the same
(then they are “like terms”). Otherwise, you can’t add or subtract them.
3. To multiply monomials, you reorganize all the factors so that you just multiply the constants
and like variables separately. You will have to use exponent rules to simplify the variable part.
4. To divide monomials, you just cancel common factors to simplify the fraction, dealing with
constants and like variables one type at a time. Remember to express your final answer with no
negative exponents.
5. Be able to multiply and divide numbers in scientific notation and then express your answer in
scientific notation.
