Transcript 7-1

7-1 Integer Exponents
Warm Up(Add to Notes)
Evaluate each expression for the given
values of the variables.
1. x3y2 for x = –1 and y = 10
2.
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for x = 4 and y = (–7)
–100
7-1 Integer Exponents
7-1 Integer Exponents
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7-1 Integer Exponents
Remember!
Base
x
4
Exponent
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7-1 Integer Exponents
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Notice the phrase “nonzero number” in the
previous table. This is because 00 and 0 raised to
a negative power are both undefined.
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7-1 Integer Exponents
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
cup is equal to
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7-1 Integer Exponents
Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
7º = 1
C. (–5)–4
D. –5–4
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Any nonzero number raised to the zero
power is 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.
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7-1 Integer Exponents
Simplify.
a. 10–4
Check It Out! Example 2
b. (–2)–4
c. (–2)–5
d. –2–5
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Check It Out! Example 3a
Evaluate the expression for the given value of
the variable.
p–3 for p = 4
Substitute 4 for p.
Evaluate exponent.
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
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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.
Evaluate expressions with
exponents.
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Write the power in the
denominator as a product.
Evaluate the powers in
the product.
Simplify.
7-1 Integer Exponents
An expression that contains negative or zero
exponents is not considered to be simplified.
Expressions should be rewritten with only positive
exponents.
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.
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Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
A. 7w–4
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B.
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Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
and
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Check It Out! Example 4
Simplify.
a. 2r0m–3
rº = 1 and
b.
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c.
.
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Lesson Quiz: Part I
1. A square foot is 3–2 square yards. Simplify this
expression.
Simplify.
2. 2–6
3. (–7)–3
4. 60
5. –112
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Lesson Quiz: Part II
Evaluate each expression for the given
value(s) of the variables(s).
6. x–4 for x =10
7.
Holt Algebra 1
for a = 6 and b = 3
7-1 Integer Exponents
Warm-Up
1. A square foot is 3–2 square yards. Simplify this
expression.
Simplify.
2. 2–6
3. (–7)–3
4. 60
5. –112
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1
–121