laws of exponents

Pre-Algebra

2-7 Properties of Exponents2-7 Properties of Exponents

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

2-7 Properties of Exponents

Warm UpEvaluate.

Pre-Algebra


271. 33

2. 4 • 4 • 4 • 4

3. b2 for b = 4

4. n2r for n = 3 and r = 2

256

16

18

Pre-Algebra


Problem of the Day

Calculate 6 to the fourth power minus 56.

Pre-Algebra


Learn to apply the properties of exponents and to evaluate the zero exponent.

Pre-Algebra


The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product.

7 • 7 • 7 • 7 = 74

(7 • 7 • 7) • 7 = 73 • 71 = 74

(7 • 7) • (7 • 7) = 72 • 72 = 74

Pre-Algebra


Words Numbers Algebra

To multiply powers with the same base, keep the base and add the exponents.

bm • bn = bm + n

35 • 38 = 35 + 8 = 313

MULTIPLYING POWERS WITH THE SAME BASE

Pre-Algebra


Additional Example 1A & 1B: Multiplying Powers with the Same Base

A. 66 • 63

69

66 + 3

B. n5 • n7

n12

n5 + 7

Add exponents.

Add exponents.

Multiply. Write the product as one power.

Pre-Algebra


D. 244 • 244

C. 25 • 2

2 6

25 + 1

248

24 4 + 4

Think: 2 = 2 1

Additional Example 1: Multiplying Powers with the Same Base Continued


Add exponents.

Add exponents.

Pre-Algebra


Try This: Example 1A & 1B

A. 42 • 44

46

42 + 4

B. x2 • x3

x5

x2 + 3

Add exponents.

Add exponents.


Pre-Algebra


D. 412 • 417

C. x5 • y2

419

41 2 + 7

Try This: Example 1C & 1D


Cannot combine; the bases are not the same.

Add exponents.

x5 • y2

Pre-Algebra


Notice what occurs when you divide powers with the same base.

DIVIDING POWERS WITH THE SAME BASE


To divide powers with the same base, keep the base and subtract the exponents.

6569 – 469

64= = bm – nbm

bn=

55

53=

5 5 55 5 5 5 5

= 5 • 5 = 52=5 5 5

5 5 5 5 5

Pre-Algebra


Subtract exponents.

72

75 – 3

75

73

Additional Example 2: Dividing Powers with the Same Base

Divide. Write the product as one power.

A.

x10

x9B.

Subtract exponents.x10 – 9

x Think: x = x1

Pre-Algebra


Subtract exponents.

97

99 – 2

99

92

Try This: Example 2

Divide. Write the product as one power.

A.

B. e10

e5

Subtract exponents.e10 – 5

e5

Pre-Algebra


When the numerator and denominator have the same base and exponent, subtracting the exponents results in a 0 exponent.

This result can be confirmed by writing out the factors.

1 = 42

42 42 – 2 = 40 = 1=

=(4 • 4)(4 • 4) = 11

1 =42

2= (4 • 4)

4 (4 • 4)

Pre-Algebra


00 does not exist because 00 represents a quotient of the form

But the denominator of this quotient is 0, which is impossible, since you cannot divide by 0.

Helpful Hint

0n

0n.

Pre-Algebra


THE ZERO POWER


The zero power of any number except 0 equals 1.

1000 = 1

(–7)0 = 1a0 = 1, if a 0

Pre-Algebra


A light-year, or the distance light travels in one year, is almost 1018 centimeters. To convert this number to kilometers, you must divide by 105. How many kilometers is a light-year?

10 18 - 5

A light-year is almost 1013 km.

10

13

10 18

10 5

Subtract exponents.

Additional Example 3: Astronomy Application

Pre-Algebra


A ship has 107 kilograms of grain loaded into its cargo hold. A metric ton is 103 kilograms. How many metric tons of grain were loaded?

10 7 - 3

The ship had 104 metric tons of grain loaded.

10

4

10 7

10 3

Subtract exponents.

The weight in metric tons is equal to the weight in kilograms divided by 10 kilograms per metric ton.3

Try This: Example 3

Pre-Algebra


Lesson Quiz: Part 1

Write the product or quotient as one power

3.

8 9

n 71. n3 n4

109

105 10 4

4.

t 2

5. 33 • 32 • 35 3 10

2. 8 • 88

t9

t7

Pre-Algebra


A school would like to purchase new globes. They can get six dozen for $705.80 from Company A. From Company B, they can buy a half gross for $725.10. Which company should they buy from? (1 gross = 122 items)

Lesson Quiz: Part 2

Company A

6.

laws of exponents

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