1. 2-7 Properties of Exponents Warm Up Problem of the Day
Lesson Presentation
Pre-Algebra

2. 2-7 Properties of Exponents Warm Up Evaluate. 1. 33 27
Pre-Algebra
2-7
Properties of Exponents
Warm Up
Evaluate.
1. 33 27
2. 4 • 4 • 4 • 4
256
3. b2 for b = 4 16
4. n2r for n = 3 and r = 2 18

3. Problem of the Day
Calculate 6 to the fourth power minus 56.

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

5. The factors of a power, such as 74, can be grouped in different ways
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

6. MULTIPLYING POWERS WITH THE SAME BASE
Words
Numbers
Algebra
To multiply powers with the same base, keep the base and add the exponents.
bm • bn = bm + n
35 • 38 = = 313
MULTIPLYING POWERS WITH THE SAME BASE

7. Additional Example 1A & 1B: Multiplying Powers with the Same Base
Multiply. Write the product as one power.
A. 66 • 63 6
6 + 3
Add exponents. 6 9
B. n5 • n7 n
5 + 7
Add exponents. n 12

8. Additional Example 1: Multiplying Powers with the Same Base Continued
Multiply. Write the product as one power.
C. 25 • 2 2
5 + 1
Think: 2 = 2 1 2 6
Add exponents.
D. 244 • 244 24
4 + 4
Add exponents. 24 8

9. A. 42 • 44 4 Add exponents. 4 B. x2 • x3 x Add exponents. x
Try This: Example 1A & 1B
Multiply. Write the product as one power.
A. 42 • 44 4
2 + 4
Add exponents. 4 6
B. x2 • x3 x
2 + 3
Add exponents. x 5

10. Cannot combine; the bases are not the same.
Try This: Example 1C & 1D
Multiply. Write the product as one power.
C. x5 • y2
Cannot combine; the bases are not the same.
x5 • y2
D. 412 • 417 41
2 + 7
Add exponents. 41 9

11. DIVIDING POWERS WITH THE SAME BASE
Notice what occurs when you divide powers with the same base. 5 53 =
5  5  5
5  5  5  5  5
= 5 • 5
= 52
DIVIDING POWERS WITH THE SAME BASE
Words
Numbers
Algebra
To divide powers with the same base, keep the base and subtract the exponents. 6 5
9 – 4 9 4 = b
m – n m n

12. Additional Example 2: Dividing Powers with the Same Base
Divide. Write the product as one power. 7 5 3 A. 7
5 – 3
Subtract exponents. 7 2 x 10 9 B. x
10 – 9
Subtract exponents. x
Think: x = x 1

13. A. B. 9 9 9 Subtract exponents. 97 e e e Subtract exponents. e
Try This: Example 2
Divide. Write the product as one power. 9 9 A. 9 2 9
9 – 2
Subtract exponents. 97 e 10 B. e 5 e
10 – 5
Subtract exponents. e 5

14. This result can be confirmed by writing out the factors.
When the numerator and denominator have the same base and exponent, subtracting the exponents results in a 0 exponent.
1 = 4 2
42 – 2 = 40 = 1 =
This result can be confirmed by writing out the factors. =
(4 • 4)
= 1 1 4 2

15. 0 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 .

16. THE ZERO POWER Words Numbers Algebra
The zero power of any number except 0 equals 1.
1000 = 1
(–7)0 = 1
a0 = 1, if a  0

17. Additional Example 3: Astronomy Application
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 10
18 - 5
Subtract exponents. 10 13
A light-year is almost 1013 km.

18. The ship had 104 metric tons of grain loaded.
Try This: Example 3
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?
The weight in metric tons is equal to the weight in kilograms divided by 10 kilograms per metric ton. 3 10 7 3 10
7 - 3
Subtract exponents. 10 4
The ship had 104 metric tons of grain loaded.

19. Lesson Quiz: Part 1
Write the product or quotient as one power
1. n3  n4 n 7
2. 8 • 88 8 9
109
105 3. 10 4 t9 t7 t 2 4.
5. 33 • 32 • 35 3 10

20. Lesson Quiz: Part 2 6.
A school would like to purchase new globes. They can get six dozen for $ from Company A. From Company B, they can buy a half gross for $ Which company should they buy from? (1 gross = 122 items)
Company A