Exploring Polynomials

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Lesson 10-1 Warm-Up
LESSON 10-1 Warm Up
2
Lesson 10-1 Warm-Up
LESSON 10-1 Warm Up
3
Properties of Exponents (10-1)

• How do you multiply numbers with the same base?
• How do you multiply powers in algebraic
  expressions?

• Rule When you multiply exponents with the same
  nonzero base (a ? 0), add the exponents.
• Example 23 24 (2 2 2) (2 2 2 2)
  27
• Example -2x 3x5 -2 3 x1 x5 -6x6
• To multiply power in algebraic expressions,
  multiply the coefficients together and add the
  exponents of like terms (same variables)
  together.
• Example
• Example

am an amn
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Properties of Exponents
LESSON 10-1
Additional Examples
Write the expression using a single exponent.
(3)2 (3)4
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Properties of Exponents
LESSON 10-1
Additional Examples
Rewrite each expression using each base only
once.
73 72
a.
44 41 42
b.
68 68
c.
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Properties of Exponents
LESSON 10-1
Additional Examples
Simplify each expression.
p2 p p5
a.
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Properties of Exponents (10-1)

• How do you divide powers with the same base?

• Rule When you divide numbers with the same base,
  subtract the exponents.
• Example a2

am am - n an
1 1 a4 a a a a a2
a a 1 1
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Properties of Exponents
LESSON 10-1
Additional Examples
Simplify each expression.
a.
b.
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Properties of Exponents (10-1)

• How do you divide numbers in scientific notation
  form?

• Rule When you divide numbers in scientific
  notation, divide the decimals and the exponents
  separately.
• Example
• To
  find average, divide the number of tons by
  number of people

10
Properties of Exponents
LESSON 10-1
Additional Examples
A small dogs heart beats about 64 million beats
in a year. If there are about 530 thousand
minutes in a year, what is its average heart rate
in beats per minute?
The dogs average heart rate is about 121 beats
per minute.
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Properties of Exponents
LESSON 10-1
Lesson Quiz
1. Write (8)4 (8)5 using a single
exponent. 2. Write using a single
exponent. 3. Jupiters diameter is about 1.43 x
105 kilometers. Earths diameter is about
1.28 x 104 kilometers. How many times greater is
Jupiters diameter than Earths diameter?
Round the answer to the nearest tenth.

(8)9
93
11.2 times greater