Unit 2 Study Guide
 Exponents:
Product rule: (Xa)( Xb )= Xa+b. Remember to keep the base and _______ the
exponents.
Power rule: (Xa)b = Xab. Remember to keep the base and ________ the exponents.
Quotient rule: Xa / Xb = Xa-b. Remember to keep the base and ________ the
exponents.
Negative exponent rule: X-a = 1/X3. Remember if the exponent is negative, in
order to make the exponent positive we must take the ___________.
Zero rule: X0= ___. Remember any number raised to zero equals ________.
** In order for all of these rules to be true we must have like_______?
Be sure you are able to prove all of these rules.
For example: Prove that (X4)(X5) = X9
Example Problems:
Simplify using exponent rules.
1. (x3)(x7) ______
2. (33)4 _________
4. a5 ÷ a9 _ ______ 5. 68 ÷ 6-3 _______
7. (a6)-4 __________
3. (2x5y)(4x-3y4) ________
6. (24xy5) ÷ (6x3y4) ______
8. x-8 _________
9. (a4b5)0 x (a2b3)__________
 Scientific notation
Be able to convert from scientific notation to standard notation and vice versa.
Scientific notation is a way to write numbers that are too big or too small to write as a
decimal.
Write in standard form.
4.5 x 105 ______________
6.9 x 10-3 _____________
Write in scientific notation.
56,000 ______________
0.0000032 ____________
To add or subtract in scientific notation the power of ten must have the same exponent.
Find the smallest exponent and move the decimal to the left the amount of spaces it
takes to change the exponent to the larger exponent. Add the numbers with the same
power of 10.
(4.9 x 107 ) + (7.3 x 107 )
(5.4 x 10−2 ) – (6.9 x 106 )
(4.1 x 106 ) + (6.8 x 105 )
(7.6 x 107 ) – (5.4 x 109 )
To multiply or divide in scientific notation there are three steps. 1. Multiply or divide
the first factors depending on the type of problem. 2. Multiply or divide the powers of
10 (remember this is where we use either the quotient or the product rule). 3. Put
answer in scientific notation.
(2 x 103)(3 x 102)
(2 x 103)(3.4 x 10-8)
(5.2 x 1013)÷ (1.3 x 107)
(4.6 x 10-4)÷ (3.1 x 102)
 Square Roots
Perfect square roots solve to a whole number, imperfect square roots solve to a
decimal.
Find the square root of the following numbers:
25
64
196
169
225
400
 Imperfect Square roots
Find the square root of these numbers:
61
96
45
55
160
115
220
 Rational/ Irrational numbers
Be able to determine if a number is rational or irrational. Also be able to tell if the
rational number is a natural number, whole number, or integer.
6
7
4
π
√-11 √69
√15
 Equations:
One step
Two step
Multi step
Variables on both side
Be able to determine the number of solutions of an equation
Your workbook page 125 will be a great tool for equation help.
Also remember the little quizzes and videos on the online textbook.