Download Chapter 1 Mid-Chapter Test Study Guide - 16

Chapter 1 Mid-Chapter Test
Study Guide
Scheduled for: Tuesday, January 24th
Topics on Test:
-Multiplying & Dividing Monomials (Lesson 3)
-Powers of Monomials (Lesson 4)
-Negative Exponents (Lesson 5)
Laws of Exponents
Law #1 Multiplying Monomials  When we are multiplying numbers or
variables with the SAME BASES we ADD the exponents
Examples
26 • 25= 25+6=11 = 211
b³ • b² = b³+²= b5
3x³•y²•x3= 3x6y²
(4x²)(3x³) = 12x5  MULTIPLY THE WHOLE NUMBERS then add
exponents!
Law #2 Dividing Monomials When we are dividing numbers or variables
with the SAME BASES we subtract the exponents
Example
x6 t5
x3 t4
=
x3t1 or x3t (either answer is fine!)
Examples
25s3 x5
5s2 x4 = 5s1x1 or 5sx
(either answer is fine!)
42 m6 x
7 m4 x = 6m2
**Where did the “x” go? Remember no exponent you plug in
and 1 - 1= 0
1
for each variable
Law #3 Power to Power When we are working with a power to a power
we multiply the exponents
Example
(72)3 = 76 or 117,649
(d7)6 = d42
Law #4 Product to Power When we are working with a product to a
power we apply the power to EACH factor (including any integers in the
problem) and then multiply each.
Example
(7a5b6)4 = 74a20b24 = 2,401a20b24
(-3w3z8)5 = -35w15z40 = -243w15z40
Negative Exponents
Write using Positive Exponents
If a number is being raised to a negative exponent, move it
in to the denominator to become a positive exponent.
More Examples:
4-5 =
m-9 =
(-2)-6 =
Evaluating Negative Exponents
Solve out and write using a positive exponent
Examples:
(-5)-5 =
-
3-2 =
(-9)-4 =
More with Negative Exponents
To write this expression using negative exponents, bring the number t
that is in the denominator up to the numerator and make it negative
It will now be: 5-2
Rewrite the denominator using an exponent that is not 1. 36=62. So now the
fraction is
. Then move it back up and change the sign to be a negative.
So the answer is 6-2.
Multiplying and Dividing with Negative Exponents
Step 1: Follow Law #1 (if multiplying) or Law #2 (if dividing)
Step 2: If your exponent is POSITIVE  leave your answer
alone! If your exponent is NEGATIVE  flip the fraction to
make it a positive!
Examples:
2-6  23 = 2-3 =
(FLIP)
(-6 + 3 = -3)
s-5  s7 = s2 (LEAVE ALONE)
(-5 + 7 = 2)
Y-3  Y3 = Y0 = 1
(-3 + 3 = 0)
= m12 (LEAVE ALONE)
[8 – (-4) = 12]
= 6-12 =
[(-4) – 8 = -12]
(FLIP)