Exponents and Scientific Notation5.15.1

1. Evaluate exponential forms with integer exponents.2. Write scientific notation in standard form.3. Write standard form numbers in scientific notation.

Objective 1

Evaluate exponential forms with integer exponents.

When an equation in one variable is solved the answer is a point on a line.

Identify the base, exponent and evaluate.Identify the base, exponent and evaluate.

Base:

Exponent:

Value:

52

42

32

42

Base:

Exponent:

Value:

Base:

Exponent:

Value:

Base:

Exponent:

Value:

2

5

32

-2

3

-8

-2

4

16

2

4

-16

Evaluate: – 32

a) 9

b) –6

c) 6

d) 9

Evaluate: – 32

a) 9

b) –6

c) 6

d) 9

Evaluate:

a) -93

43253 2

b) 15

c) 105

d) None of the above

Evaluate:

a) -93

43253 2

b) 15

c) 105

d) None of the above

Evaluating Exponential Forms with Negative Bases

(negative number)even exponent = positive

(negative number)odd exponent = negative

When an equation in one variable is solved the answer is a point on a line.

Evaluate.Evaluate.

3

52

2

53

125

8

259

Raising a Quotient to a Power

If a and b are real numbers, where b 0 and n is a natural number, then

.

n n

n

a a

b b

0

1

2

3

4

3

33

93

273

813Observe the pattern….

1

Zero as an Exponent

If a is a real number and then 0,a 0 1.a

When an equation in one variable is solved the answer is a point on a line.

Evaluate:Evaluate:

05

05

05

0

251

1 1

– 1 1

When an equation in one variable is solved the answer is a point on a line.

Evaluate:Evaluate:

06y

07

06y

00 43

61

– 1

1 – 1 = 0

When an equation in one variable is solved the answer is a point on a line.

Evaluate:Evaluate:

020 268 yxw

033 Indeterminate

-6x2

13

33

93

273

813

0

1

2

3

4

Observe the pattern….

33

22

11

3

1271

3

3

191

3

3

131

3

Negative exponents are POSITIONAL only!!!Negative exponents are POSITIONAL only!!!

If a is a real number, where a 0 and n is a natural

number, then 1

. nn

aa

Exponents must be positive before you can evaluate!!!

When an equation in one variable is solved the answer is a point on a line.

Simplify:Simplify:

32

34 x

23 x

35x

81

2

13 2

3

x

34

x

35x

35x

35 x 31

5x

1

53x

35x

Negative exponents are POSITIONAL only!!!Negative exponents are POSITIONAL only!!!

If a is a real number, where a 0 and n is a natural number, then

1. n

na

a

When an equation in one variable is solved the answer is a point on a line.

Simplify:Simplify:

2

32

b

a

3233 yx

3

42

c

ba

km

h2

54

232

ba

2

34

a

cb

3

233

y

x

kh

m5

24

23

x 23

1

x

231

x 2

91

x

91

2x

9

2x

2

3

x

If a and b are real numbers, where a 0 and b 0

and n is a natural number, then

.

n na b

b a

Slide 5- 24Copyright © 2011 Pearson Education, Inc.

Evaluate: – 2–6

a)

b)

c)

d) 64

12

1

64

1

64

5.1

Slide 5- 25Copyright © 2011 Pearson Education, Inc.

Evaluate: – 2–6

a)

b)

c)

d) 64

12

1

64

1

64

5.1

Objective 2

Write scientific notation in standard form.

Scientific notation: A number expressed in the form where a is a decimal number with and n is an integer.

10 ,na1 10 a

3

5

10452

10453

.

.

Write 875,000 in scientific notation.

758. 510

Write 0.0000000472 in scientific notation.

724. 810

54.26 10

Write in standard form:

= 426,000

Write in standard form:

43.87 10 = .000387

Slide 5- 32Copyright © 2011 Pearson Education, Inc.

Write 13,030,000 in scientific notation.

a)

b)

c)

d)

41303 10

613.03 10

71.303 10

90.1303 10

5.1

Slide 5- 33Copyright © 2011 Pearson Education, Inc.

Write 13,030,000 in scientific notation.

a)

b)

c)

d)

41303 10

613.03 10

71.303 10

90.1303 10

5.1

Slide 5- 34Copyright © 2011 Pearson Education, Inc.

Write in standard notation.

a) 4,690,000

b) 4,690,000,000

c) 0.000000469

d) 0.00000469

64.69 10

5.1

Write in standard notation.

a) 4,690,000

b) 4,690,000,000

c) 0.000000469

d) 0.00000469

64.69 10

5.1