Download Lessons 1 - 4

Integral Exponents
Any number which can be expressed using a base
and an exponent is called a power.
3
6
Exponents are used to show repeated multiplication.
The exponent tells you how many times to use the
base as a factor.
Exponent Laws or Properties
Product Property: In multiplication, when the bases are
the same, add the exponents.
Quotient Property: In division, when the bases are the
same, subtract the exponents.
Power Property: When the base is a power, and it is
raised to another exponent,
multiply the exponents.
Exponent Laws
Power of a Product: Remember that everything within
the brackets is considered part
of the base. Apply the Power
Property to all the terms within
the brackets.
Power of a Quotient: Follow the same rules as a power
of a product.
Exponent Laws
Zero Property: Any base with a zero exponent has a
value of 1.
Negative Exponents: Change the numbers with negative
exponents to numbers with positive
exponents by reciprocating the base.
Exponent Laws
Things to watch for when evaluating powers:
Simplifying Algebraic Expressions Using the Power Laws
(2x3y2)(3x2y4) =
(3x2y2)3 x (-2x3y)2 =
(-3xy2)(-2x2y)2 =
3
 2x y 
 2 2 
3x y 
2 3
2
2x y  3xy 
 3 2  4 
 x y 2x y 
2 2
4
Evaluating Expressions Using the Power Laws
5-2
-8a0
-32
-( 3
)0
50 + 5-1
-6-2
(2-2 + 32 - 5-1)0
32 + 2 3 + 4 0
2
3
 
4 
1
1
2 3
2
3
4
 3
2 3
32
3
3
2
2
Evaluating Algebraic Expressions
Evaluate for a = 2 and b = 3:
2
1
3a b   9ab 
 2 2   2 3 
2a b  8a b 
4
3
Example:
2ab2 =
3
Rewriting Powers to a Specified Base
Express the first number as a power of the second:
81, 3
81 =
25, 5
25
Express as a power of 2:
162 x 323 x 8-4
Express as a power of 3.
272 x 814 x 93
=
2
243
Simplifying and Evaluating Expressions with Powers
1. 2a2 x 6a3
2. (3a2b3c0)3
3. -6a5 x 2a2
4. (1 - 1)3 x (-1)2
5.
(-1)9
7.
5-3
9.
a-3
11.
(-5)-2
x
(-1)4
6. -24 x -33
8. -6a0
x
a4
13. 8a10 ÷ 4a3
10. -5-2
12. (-22)3
14. -3a2b3 ÷ a-2b4
Evaluating Expressions with Powers
3-2 + 4 -1
52 + 5-1
Evaluating Expressions with Negative Exponents
23
2
2 2
(4  3 )
Or
Writing Answers With Positive Exponents
When the exponent is negative in the numerator,
move it to the denominator to make it positive.
When the exponent is negative in the denominator,
move it to the numerator to make it positive.
6a 2 b3 c 4
1 2
7d e
4a 2 b3
5c 2 d
Simplifying Expressions to a Given Power
Express as a power of 2:
32  16  8
5
32
3
4
5
Page 64 – 68:
1ac, 2, 3begi,
4-8, 10, 11, 12abcghi,
13ab,14bc, 15-18,
19bdf, 20, 21
Page 73 - 76:
1-4, 5bd, 6bde,
7, 8acfg, 9, 10,
12, 13ad
Page 80 - 83: 1, 2, 3, 4abcfg, 5,
7cdgh, 8, 9, 10bdf, 11ab, 12ac, 13acf,
14a, 15, 16
Scientific Notation
Scientific Notation is a method of expressing very large
or very small numbers in a compact form. To be in
scientific notation a number is expressed as a product of
a number between 1 and 2 and a power of 10.
1.236 x 106
1.342 x 10-5
145 320 000 000
0.000 000 000 000 046
15.26 x 107
0.024 x 10-8
Calculating with Scientific Notation
(4.3  10 )  (3.8  10 )
4
2.7  10
5
6
26 000 000 000  420 000 000 000
12 000 000 000
Page 89- 92:
1, 2, 5, 8acegi, 9ace, 10bd, 11ac, 12bd, 13, 15