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Negative Exponents

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- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

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

Odd # of Negatives = Negative

Even # of Negatives = Positive

Negative & Zero Exponents

- 22 Means… 2 • 2 = 4
- 21 Means… 2 = 2
- 20 Means… 1
- What does 2-1 Mean?

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 & 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 & Zero Exponents

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an

Negative & Zero Exponents

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an

Negative & Zero Exponents

Definition of Negative Exponent

For any integer n,

a-n is the reciprocal of an

Negative & Zero Exponents

A negative exponent is an inverse!

Flip the number over to make the exponent positive!

Simplify.

Negative & Zero Exponents

3 3 3

=

Follow the Pattern!

3 3

=

Notice that anything to the zero power is always one!

=

3

1

=

=

=

=

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 & 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 & 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 & Zero Exponents

- Zero Exponent:
- Negative Exponent:

Negative & Zero Exponents

Simplify.

Negative & Zero Exponents

Simplify.

Negative & Zero Exponents

Simplify.

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 & Zero Exponents

That's all Folks!

Take Out Your Study Guide!!!

# 4

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

# 5

- For any integer n, a-n is the
- reciprocal of an

EXAMPLES:

A negative exponent is an inverse!

# 6

Zero Exponent

- Any number to the zero power is ALWAYS ONE.
- x0 = 1

Ex: