Warm%20Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Find the product.
1. 5 5 5 5
625
27
2. 3 3 3
3. (7) (7) (7)
343
4. 9 9
81
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Vocabulary
exponential form exponent base power
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If a number is in exponential form, the exponent
represents how many times the base is to be used
as a factor. A number produced by raising a base
to an exponent is called a power. 27 and 33 are
equivalent.
Exponent
Base
7
2
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Additional Example 1 Writing Exponents
Write in exponential form.
A. 4 4 4 4
Identify how many times 4 is a factor.
B. (6) (6) (6)
Identify how many times 6 is a factor.
(6) (6) (6) (6)3
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Additional Example 1 Writing Exponents
Write in exponential form.
Identify how many times 5 and d are each used as
a factor.
C. 5 5 d d d d
5 5 d d d d 52d4
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Check It Out! Example 1
Write in exponential form.
A. x x x x x
Identify how many times x is a factor.
B. d d d
Identify how many times d is a factor.
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Check It Out! Example 1
Write in exponential form.
C. 7 7 b b
Identify how many times 7 and b are each used as
a factor.
7 7 b b 72b2
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Additional Example 2 Simplifying Powers
Simplify.
35 3 3 3 3 3
Find the product.
243
B.
Find the product.
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Additional Example 2 Simplifying Powers
Simplify.
Find the product.
256
Find the product. Then make the answer negative.
28 (2 2 2 2 2 2 2 2)
256
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Check It Out! Example 2
Simplify.
74 7 7 7 7
Find the product.
2401
Find the product.
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Check It Out! Example 2
Evaluate.
Find the product.
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Find the product. Then make the answer negative.
94 (9 9 9 9)
6,561
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Additional Example 3 Using the Order of
Operations

Substitute 4 for x, 2 for y, and 3 for z.
4(24 32) 42
4(16 9) 16
Simplify the powers.
4(7) 16
Subtract inside the parentheses.
Multiply from left to right.
28 16
Add.
44
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Check It Out! Example 3


Substitute 5 for x, 2 for y, and 60 for z.
60 7(25 52)
60 7(32 25)
Simplify the powers.
60 7(7)
Subtract inside the parentheses.
60 49
Multiply from left to right.
Subtract.
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Additional Example 4 Geometry Application
Use the expression (n2 3n) to find the
number of diagonals in a 7-sided figure.
Substitute the number of sides for n.
Simplify inside the parentheses.
Subtract inside the parentheses.
14 diagonals
Multiply.
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Additional Example 4 Continued
A 7-sided figure has 14 diagonals. You can verify
your answer by sketching the diagonals.
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Check It Out! Example 4
Use the expression (n2 3n) to find the
number of diagonals in a 4-sided figure.
Substitute the number of sides for n.
Simplify inside the parentheses.
Subtract inside the parentheses.
2 diagonals
Multiply
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Check It Out! Example 4 Continued
A 4-sided figure has 2 diagonals. You can verify
your answer by sketching the diagonals.
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Lesson Quiz
Write in exponential form.
1. n n n n
2. (8) (8) (8) (h)
(8)3h
Simplify.
256
3. (4)4
4.
5. Evaluate xz yx for x 5, y 3, and z 6.
213
6. A population of bacteria doubles in size every
minute. The number of bacteria after 5 minutes is
15 ? 25. How many are there after 5 minutes?
480