Page 212 - Algebra 1

L E S S O N Simplifying and Evaluating Expressions with
Integer and Zero Exponents
32
Warm Up
NewConcepts
1. Vocabulary The of a power is the number used as a factor. (3)
Simplify. 2. 34
(3)
4. 26 + (-18) (5)
3. x5 · x6 (3)
5. -34 - 19 (6)
Algebraicexpressionsmaycontainexponentsthatarepositive,negative,orzero. The relationship between the different exponents can be understood by looking at successive powers of a positive integer greater than 1. Look at the powers of 2.
Power of 2 Value
24 =16 23 =8 22 =4 21 =2
In the left column, each entry is found by decreasing the exponent in the previous entry by one. In the right column, each entry is found by halving the previous entry, or by dividing it by 2. Use this pattern to find the next three powers.
Math Reasoning
Verify Show why 24 = 16.
Power of 2
24 23 22 21 20
2-1 2-2
Value
=16
=8
=4
=2
=1
= _1or_1 2 21
= _1or_1 4 22
The pattern illustrates the properties for negative and zero exponents.
An algebraic expression is not considered simplified if it contains negative or zero exponents. The Product Property of Exponents applies to negative and zero exponents.
Negative and Zero Exponent Properties
Negative Exponent Property
_1 n
For every nonzero number x, x-n = xn and x = x-n .
1 _
Zero Exponent Property
For every nonzero number x, x0 = 1.
Math Language
The Product Property of Exponents states that the exponents of powers with the same base are added.
x3 ·x4 =x3+4 =x7
Lesson 32 197