7-1 Integer Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards...
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Transcript of 7-1 Integer Exponents Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards...
7-1 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)
7-1 Integer Exponents
2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
California Standards
7-1 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 make a conjecture.
3125 625 125 25 5
5
Power
Value
55 54 53 52 51 5–150 5–2
5 5 5
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.
7-1 Integer Exponents
Notice the phrase “nonzero number” in the
previous table. This is because 00 and 0 raised to
a negative power are both undefined. For
example, if you use the pattern given above in
the table with a base of 0 instead of 5, you would
get 00 = . Also, 0–6 would be = . Since
division by 0 is undefined, neither value exists.
7-1 Integer ExponentsAdditional Example 1: Measurement Application
One cup is 2–4 gallons. Simplify this expression.
gal is equal to
7-1 Integer ExponentsCheck It Out! Example 1
A sand fly may have a wingspan up to 5–3 m. Simplify this expression.
5-3 m is equal to
7-1 Integer ExponentsAdditional Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
7º = 1 Any nonzero number raised to the zero power is 1.
C. (–5)–4
D. –5–4
7-1 Integer Exponents
In (–3)–4, the base is negative because the
negative sign is inside the parentheses. In –3–4
the base (3) is positive.
Caution
7-1 Integer ExponentsAdditional Example 3A: Evaluating Expressions with
Zero and Negative Exponents
Evaluate the expression for the given value of the variable.
x–2 for x = 4
Substitute 4 for x.
Use the definition
7-1 Integer ExponentsAdditional Example 3B: Evaluating Expressions with Zero
and Negative ExponentsEvaluate 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.
7-1 Integer ExponentsCheck 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.
7-1 Integer ExponentsCheck It Out! Example 3b
Evaluate the expression for the given values of the variables.
for a = –2 and b = 6
2
Substitute –2 for a and 6 for b.
Evaluate expressions with exponents.
Write the power in the denominator as a product.
Evaluate the powers in the product.
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.
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.
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.
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.
7-1 Integer Exponents
Simplify.
Additional Example 4: Simplifying Expressions with Zero and Negative Numbers
A. 7w–4 B.
7-1 Integer Exponents
Simplify.
Additional Example 4: Simplifying Expressions with Zero and Negative Numbers
C.
and
7-1 Integer ExponentsLesson 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
1
–121