32 integer exponents warm up evaluate each expression for the given values of the variables. 1. x 3...
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32 Integer Exponents
Warm UpEvaluate each expression for the given values of the variables.
1. x3y2 for x = –1 and y = 10
2. for x = 4 and y = (–7)
Write each number as a power of the given base.
–100
433. 64; base 4
(–3)34. –27; base (–3)
32 Integer Exponents
Evaluate expressions containing zero and integer exponents.
Simplify expressions containing zero and integer exponents.
Learning Targets
32 Integer Exponents
You have seen positive exponents. Recall that to simplify 32, use 3 as a factor 2 times: 32 = 3 3 = 9.
But what does it mean for an exponent to be negative or 0? You can use a table and look for a pattern to figure it out.
3125 625 125 25 5
5
Power
Value
55 54 53 52 51 5–150 5–2
5 5 5
32 Integer Exponents
32 Integer Exponents
https://www.khanacademy.org/math/arithmetic/exponents-radicals/negative-exponents-tutorial/v/zero--negative--and-fractional-exponents
32 Integer Exponents
Zero and Negative Exponents
Simplify.
A. 4–3
B. y0
yº = 1
C. (–5)–4
D. –5–4
32 Integer Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7719/7719.xml
32 Integer Exponents
On Your OwnSimplify.
a. 10–4
b. (–2)–4
c. (–2)–5
d. –2–5
32 Integer Exponents
What if you have an expression with a negative
exponent in a denominator, such as ?
or Definition of a negative exponent.
Substitute –8 for n.
Simplify the exponent on the right side.
So if a base with a negative exponent is in a denominator, it is equivalent to the same base with the opposite (positive) exponent in the numerator.
An expression that contains negative or zero exponents is not considered to be simplified. Expressions should be rewritten with only positive exponents.
32 Integer Exponents
Simplify.
Example 1: Simplifying Expressions with Zero and Negative Numbers
A. 7w–4 B.
32 Integer Exponents
Simplify.
C.
and
32 Integer Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7721/7721.xml
32 Integer Exponents
On your own Example 1
Simplify.
a. 2r0m–3
b.
c.
32 Integer Exponents
Example 2: Evaluating Expressions with Zero and Negative Exponents
Evaluate the expression for the given value of the variables.
x–2 for x = 4
Substitute 4 for x.
Use the definition
32 Integer Exponents
Evaluate the expression for the given values of the variables.
–2a0b-4 for a = 5 and b = –3
Substitute 5 for a and –3 for b.
Evaluate expressions with exponents.
Write the power in the denominator as a product.
Evaluate the powers in the product.
Simplify.
32 Integer Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=7720/7720.xml
32 Integer Exponents
On your own! Example 2
Evaluate the expression for the given value of the variable.
3b-3b b = -3
32 Integer Exponents
On your own! Example 2
Evaluate the expression for the given values of the variables.
for a = –2 and b = 6
32 Integer Exponents
32 Integer Exponents
https://www.khanacademy.org/math/arithmetic/exponents-radicals/exponent-properties/v/exponent-properties-involving-quotients
32 Integer Exponents
Simplify.
Example 3: Finding Quotients of Powers
A. B.
32 Integer Exponents
C.
Simplify.
D.
32 Integer Exponents
http://my.hrw.com/math11/math06_07/nsmedia/lesson_videos/alg1/player.html?contentSrc=6360/6360.xml
32 Integer Exponents
Check It Out! Example 1
Simplify.
c. d.