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# Negative Exponents - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' Negative Exponents' - melba

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and

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

• 22 Means… 2 • 2 = 4

• 21 Means… 2 = 2

• 20 Means… 1

• What does 2-1 Mean?

• 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!

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.

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an

A negative exponent is an inverse!

Flip the number over to make the exponent positive!

Simplify.

3 3 3

=

3 3

=

Notice that anything to the zero power is always one!

=

3

1

=

=

=

=

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

Study the table and FOLLOW THE PATTERN!

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

Study the table and FOLLOW THE PATTERN!

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

• Zero Exponent:

• Negative Exponent:

Simplify.

Simplify.

Simplify.

Identity Property

Why It Works

2

-2

3

3

9

x0 = 1

9

=

1

Any number to the zero power is ALWAYS ONE.

That's all Folks!

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

• For any integer n, a-n is the

• reciprocal of an

EXAMPLES:

A negative exponent is an inverse!

Zero Exponent

• Any number to the zero power is ALWAYS ONE.

• x0 = 1

Ex: