6th Grade Math Textbook, Fundamentals

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Lesson 1-9 for exercise sets. &KDSWHU 

Write each in simplest exponential form.

1.6 • 6 • 6 • 7 • 7 2.1(1)(2)(3)(3) 3.2 • 2^2 • 2^4 4.

Write each in factored form. Then simplify.

5. 43 6. 20 7. 109  105 8. 51 • 5^3

9.Discuss and Write Explain how patterns and place value can be used to

show that any nonzero number to the zero power is equal to 1.

56

52

Key Concept

am• anamn, where a 0

Law of Exponents for Multiplication

Key Concept

amanamn, where a 0

Law of Exponents for Division

Key Concept

a^0 1, where a 0

Law of Exponents for Zero

While  52 and (5)^2 may appear

to be the same, they actually have

different meanings and different

values.

 52 means “the opposite of five

squared.”

 52 (5 • 5)  25

(5)^2 means “negative five squared.”

(5)^2 (5)(5)  25

You can write powers in standard form by expressing the

power in factored form and then multiplying the factors.

Simplify: (5)^2 • 10^2

(5)^2 • 10^2 (5)(5)• (10)(10)

25 • 100 Multiply.

 2500

The can help you simplify expressions.

• To multiply two powers that have the same base,
  keep the base and add the exponents.
  Simplify: 6^3 • 6^5
  63 • 6^5 (6 • 6 • 6) • (6 • 6 • 6 • 6 • 6)
   68
  Or 6^3 • 6^5  63 ^5
   68


• To divide two powers that have the same base,
  keep the base and subtract the exponents.

Simplify:



3 • 3 • 3 • 3

 34

Or  36 ^2  34

• A number to the zero power always equals 1.

Simplify:



 1

Or  36 ^6  30  1

Apply the Law of Exponents for Division.

333333

333333

111111

111111

•••••

•••••

333333

33

11

11

•••• •

Laws of Exponents

36

36

36

36

36

36

36

32

36

32

36

32

Express each power

in factored form.