Transcript Slide 1
7-1 Integer Exponents Warm Up Evaluate each expression for the given values of the variables.
1. x 3
y
2 for x = –1 and y = 10 –100
2.
for x = 4 and y = (–7)
Write each number as a power of the given base.
3. 64; base 4 4. –27; base (–3) 4 3 (–3) 3
Holt McDougal Algebra 1
7-1 Integer Exponents
Objectives
Evaluate expressions containing zero and integer exponents.
Simplify expressions containing zero and integer exponents.
Holt McDougal Algebra 1
7-1 Integer Exponents
You have seen positive exponents. Recall that to simplify 3
2
, use 3 as a factor 2 times: 3 2 = 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.
Power Value
5 5 5 4 5 3 5 2 3125 625 125 25 5 5 5 5 5 1 5 5 0 5 –1 5 –2
Holt McDougal Algebra 1
7-1 Integer Exponents
When the exponent decreases by one, the value of the power is divided by 5. Continue the pattern of dividing by 5.
Holt McDougal Algebra 1
7-1 Integer Exponents Remember!
Base
x
4 Exponent Holt McDougal Algebra 1
7-1 Integer Exponents Holt McDougal Algebra 1
7-1 Integer Exponents
Notice the phrase “ nonzero number ” in the previous table. This is because 0 0 and 0 raised to a negative power are both undefined. For example, if you use the pattern given above the table with a base of 0 instead of 5, you would get 0º = . Also 0 –6 would be = . Since division by 0 is undefined, neither value exists.
Holt McDougal Algebra 1
7-1 Integer Exponents Reading Math
2 –4 is read “ 2 to the negative fourth power.
”
Holt McDougal Algebra 1
7-1 Integer Exponents Example 1: Application One cup is 2 –4 gallons. Simplify this expression.
gal is equal to
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7-1 Integer Exponents Check It Out!
Example 1 A sand fly may have a wingspan up to 5 –3 Simplify this expression.
m.
5 -3 m is equal to
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7-1 Integer Exponents Example 2: Zero and Negative Exponents Simplify.
A. 4 –3 B. 7 0
7º = 1
C. (–5) –4
Any nonzero number raised to the zero power is 1.
D. –5 –4 Holt McDougal Algebra 1
7-1 Integer Exponents Caution
In (–3) –4 , the base is negative because the negative sign is inside the parentheses. In –3 –4 the base (3) is positive.
Holt McDougal Algebra 1
7-1 Integer Exponents Simplify.
a. 10 –4 Check It Out!
Example 2 b. (–2) –4 c. (–2) –5 d. –2 –5 Holt McDougal Algebra 1
7-1 Integer Exponents Example 3A: 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
Holt McDougal Algebra 1
7-1 Integer Exponents Example 3B: Evaluating Expressions with Zero and the variables.
–2a 0
b
-4 Negative Exponents Simplify the expression for the given values of 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.
Simplify the denominator.
Simplify.
Holt McDougal Algebra 1
7-1 Integer Exponents Check It Out!
Example 3a Evaluate the expression for the given value of the variable.
p
–3 for p = 4
Substitute 4 for p.
Simplify exponent.
Write the power in the denominator as a product.
Simplify the denominator.
Holt McDougal Algebra 1
7-1 Integer Exponents Check It Out!
Example 3b Evaluate the expression for the given values of the variables.
for a = –2 and b = 6
Substitute –2 for a and 6 for b.
Simplify expressions with exponents.
Write the power in the denominator as a product.
Simplify the denominator.
2
Holt McDougal Algebra 1
Simplify.
7-1 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.
Holt McDougal Algebra 1
7-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify.
A. 7w –4 B. Holt McDougal Algebra 1
7-1 Integer Exponents Example 4: Simplifying Expressions with Zero and Negative Numbers Simplify.
C.
and
Holt McDougal Algebra 1
7-1 Integer Exponents Check It Out!
Example 4 Simplify.
a. 2r 0
m
–3
rº = 1 and .
b.
c.
Holt McDougal Algebra 1
7-1 Integer Exponents Lesson Quiz: Part I
1. A square foot is 3 –2 expression. square yards. Simplify this
Simplify.
2. 2 –6 3. (–7) –3 4. 6 0 5. –11 2 1 –121
Holt McDougal Algebra 1
7-1 Integer Exponents Lesson Quiz: Part II Evaluate each expression for the given value(s) of the variables(s).
6. x –4 for x =10
7.
for a = 6 and b = 3
Holt McDougal Algebra 1
7-1 Integer Exponents Holt McDougal Algebra 1