Negative Exponents
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Negative Exponents. and. Zero Exponents. Negative & Zero Exponents. Multiply Integers REVIEW. = + 1. 1 • 1. 1 • -1. = - 1. -1 • -1. = + 1. -1 • -1 • -1. = - 1. -1 • -1 • -1 • -1. = + 1. -1 • -1 • -1 • -1 • -1. = - 1. -1 • -1 • -1 • -1 • -1 • -1. = + 1.

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Negative Exponents

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Negative exponents

Negative Exponents

and

Zero Exponents


Negative exponents

Negative & Zero Exponents

Multiply Integers REVIEW

= +1

1 • 1

1 • -1

= -1

-1• -1

= +1

-1• -1 • -1

= -1

-1 •-1• -1 • -1

= +1

-1 •-1 •-1• -1 • -1

= -1

-1 •-1 •-1 •-1• -1 • -1

= +1

Odd # of Negatives = Negative

Even # of Negatives = Positive


Negative exponents

Negative & Zero Exponents

  • 22 Means… 2 • 2 = 4

  • 21 Means… 2 = 2

  • 20 Means… 1

  • What does 2-1 Mean?


Negative exponents

Negative & Zero Exponents

  • What does 2-1 Mean?

  • You cannotleave an exponent negative because there is no way to express it’s meaning.

  • You must make it positive!


Negative exponents

Negative & Zero Exponents

You do NOT want to have negative exponents in your answer. You get rid of them by flipping the exponent over, like reciprocals.

If the negative exponent is on top, move it to the bottom.


Negative exponents

Negative & Zero Exponents

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an


Negative exponents

Negative & Zero Exponents

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an


Negative exponents

Negative & Zero Exponents

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an


Negative exponents

Negative & Zero Exponents

A negative exponent is an inverse!

Flip the number over to make the exponent positive!

Simplify.


Negative exponents

Negative & Zero Exponents

3 3 3

=

Follow the Pattern!

3 3

=

Notice that anything to the zero power is always one!

=

3

1

=

=

=

=


Negative exponents

Negative & Zero Exponents

Follow the Pattern!

1

10

10

10

10

10

10

-1

1

10

= 0.1

10

1

2

100

3

-2

1

10

1

100

= 0.01

1,000

10

2

4

10,000

-3

1

10

1

1000

= 0.001

10

5

100,000

3


Negative exponents

Negative & Zero Exponents

Study the table and FOLLOW THE PATTERN!

Exponent, n 25 24 23 22 21 20 2–1 2–2 2–3Power, 2n

1

2

1

4

1

8

32

16

8

4

2

1

What do you think 2–4 will be?

2–4 = 1 = 1

2416

What do you think 2–5 will be?

2–5 = 1 = 1

2532


Negative exponents

Negative & Zero Exponents

Study the table and FOLLOW THE PATTERN!

Exponent, n 35 34 33 32 31 30 3–1 3–2 3–3Power, 3n

1

3

1

9

1

27

243

81

27

9

3

1

What do you think 3–4 will be?

3–4 = 1 = 1

3481

What do you think 3–5 will be?

3–5 = 1 = 1

35243


Negative exponents

Negative & Zero Exponents

  • Zero Exponent:

  • Negative Exponent:


Negative exponents

Negative & Zero Exponents

Simplify.


Negative exponents

Negative & Zero Exponents

Simplify.


Negative exponents

Negative & Zero Exponents

Simplify.


Negative exponents

Negative & Zero Exponents

Identity Property

Why It Works

2

-2

3

3

9

x0 = 1

9

=

1

Any number to the zero power is ALWAYS ONE.


Negative exponents

Negative & Zero Exponents

That's all Folks!

Take Out Your Study Guide!!!


P o w e r s o f t e n

# 4

Powers of Ten

1

10

10

10

10

10

10

-1

1

10

= 0.1

10

1

2

100

3

-2

1

10

1

100

= 0.01

1,000

10

2

4

10,000

-3

1

10

1

1000

= 0.001

10

5

100,000

3


Negative exponents

# 5

Negative Exponents

  • For any integer n, a-n is the

  • reciprocal of an

EXAMPLES:

A negative exponent is an inverse!


Negative exponents

# 6

Zero Exponent

  • Any number to the zero power is ALWAYS ONE.

  • x0 = 1

Ex:


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