1. 4-2 Warm Up Problem of the Day Lesson Presentation
Look for a Pattern in
Integer Exponents
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Evaluate.
1000 1
• 102
10,000
107
104 4.
1000
106 5. 1

3. Problem of the Day
Find two different numbers for the values of x and y that will make xy and yx equal.
2 and 4

4. Learn to evaluate expressions with negative exponents and to evaluate the zero exponent.

5. 10 2 1 –1 –2
10 • 10
100
= 0.1
= 0.01
÷ 10
÷ 10
÷ 10
÷ 10
Look for a pattern in the table to extend what you know about exponents to include negative exponents.

6. Extend the pattern from the table.
Additional Example 1A & 1B: Using a Pattern to Evaluate Negative Exponents
Evaluate the powers of 10.
A. 10–2
10–2 = 1
10 • 10
Extend the pattern from the table.
10–2 = 1
100
= 0.01
Multiply. Write as a decimal.
B. 10–1
Extend the pattern from the table.
10 = –1 1 10
10 = = 0.1 –1 1 10
Multiply. Write as a decimal.

7. Extend the pattern from the table.
Check It Out: Example 1A
Evaluate the powers of 10.
10–8
Extend the pattern from the table.
10–8 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Multiply.
10–8 = 1
100,000,000
Write as a decimal. =

8. Extend the pattern from example 1A.
Check It Out: Example 1B
10–9
Extend the pattern from example 1A.
10–9 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Multiply.
10–9 = 1
1,000,000,000
Write as a decimal. =

9. NEGATIVE EXPONENTS Remember!
The reciprocal of a number is 1 divided by that number.
Remember!

10. Additional Example 2A: Evaluating Negative Exponents
Evaluate.
5–3 5 1 3 =
Write the reciprocal; change the sign of the exponent. 1
5 • 5 • 5 =
Find the product of three ’s.
1 5
125 1 =
Simplify.

11. Additional Example 2B: Evaluating Negative Exponents
Evaluate.
(–10)–3 1
= –10 3
Write the reciprocal; change the sign of the exponent. 1
–10 • –10 • –10 =
Find the product of three ’s.
1 –10
–1000 1 =
= –0.001
Simplify.

12. Evaluate. 4–2 1 4 Check It Out: Example 2A=
Write the reciprocal; change the sign of the exponent. 1
4 • 4 =
Find the product of two ’s.
1 4 16 1 =
Simplify.

13. Evaluate. (–7)–4 Check It Out: Example 2B1
= –7 4
Write the reciprocal; change the sign of the exponent. 1
–7 • –7 • –7 • –7 =
Find the product of four ’s.
1 –7
2401 1 =
Simplify.

15. Additional Example 3: Using the Order of Operations
Evaluate 5 – (6 – 4)–3 + (– 2)0.
5 – (6 – 4)–3 + (–2)0
= 5 – (2)–3 + (–2)0
Subtract inside the parentheses.
= 5 –
1 8
Evaluate the exponents.
= 5
7 8
Add and subtract from left to right.

16. Check It Out: Example 3
Evaluate 3 + (7 – 4)–2 + (–8)0.
3 + (7 – 4)–2 + (–8)0
= 3 + (3)–2 + (–8)0
Subtract inside the parentheses. =
1 9
Evaluate the exponents.
= 4
1 9
Add.

17. Lesson Quiz
Evaluate the powers of 10.
1. 10–3
0.001
2. 10–7
Evaluate.
1 36
3. (–6)–2
4. 4 • 2–3 + 10–1
5. 80 – (11 – 24)–2
6. (4w)–2 + w–1 for w = 4