1. 4-1
Exponents
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Find the product.
1. 5 • 5 • 5 • 5
625
2. 3 • 3 • 3 27
3. (–7) • (–7) • (–7)
–343
4. 9 • 9 81

3. Problem of the Day
What two positive integers when multiplied together also equal the sum of the same two numbers?
2 and 2

4. Learn to evaluate expressions with exponents.

5. Vocabulary
exponential form
exponent
base
power

6. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. A number produced by raising a base to an exponent is called a power. Both 27 and 33 represent the same power.
Exponent
Base 7 2

7. Additional Example 1: Writing Exponents
Write in exponential form.
A. 4 • 4 • 4 • 4
Identify how many times 4 is a factor.
4 • 4 • 4 • 4 = 44
B. (–6) • (–6) • (–6)
Identify how many times –6 is a factor.
(–6) • (–6) • (–6) = (–6)3
Read –(63) as “-6 to the 3rd power” or “-6 cubed”.
Reading Math

8. Additional Example 1: Writing Exponents
Write in exponential form.
Identify how many times 5 and d are used as a factor.
C. 5 • 5 • d • d • d • d
5 • 5 • d • d • d • d = 52d4

9. Write in exponential form.
Check It Out: Example 1
Write in exponential form.
A. x • x • x • x • x
Identify how many times x is a factor.
x • x • x • x • x = x5
B. d • d • d
Identify how many times d is a factor.
d • d • d = d3

10. Write in exponential form.
Check It Out: Example 1
Write in exponential form.
C. 7 • 7 • b • b
Identify how many times 7 and b are used as a factor.
7 • 7 • b • b = 72b2

11. Additional Example 2: Evaluating Powers
Evaluate.
A. 35
Find the product of five 3’s.
35 = 3 • 3 • 3 • 3 • 3
= 243
B. (–3)5
Find the product of five –3’s.
= (–3) • (–3) • (–3) • (–3) • (–3)
(–3)5
= –243
Helpful Hint
Always use parentheses to raise a negative number to a power.

12. Additional Example 2: Evaluating Powers
Evaluate.
C. (–4)4
Find the product of four –4’s.
= (–4) • (–4) • (–4) • (–4)
(–4)4
= 256
D. 28
Find the product of eight 2’s.
28 = 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2
= 256

13. Evaluate. A. 74 Find the product of four 7’s. 74 = 7 • 7 • 7 • 7
Check It Out: Example 2
Evaluate.
A. 74
Find the product of four 7’s.
74 = 7 • 7 • 7 • 7
= 2401
B. (–9)3
Find the product of three –9’s.
= (–9) • (–9) • (–9)
(–9)3
= –729

14. Evaluate. C. –(5)2 = –(5) • (5) –(5)2 = –25 D. 97
Check It Out: Example 2
Evaluate.
C. –(5)2
Find the product of two 5’s and then make the answer negative.
= –(5) • (5)
–(5)2
= –25
D. 97
Find the product of seven 9’s.
97 = 9 • 9 • 9 • 9 • 9 • 9 • 9
= 4,782,969

15. Additional Example 3: Using the Order of Operations
Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3. y
x(yx – zy) + x y
Substitute 4 for x, 2 for y, and 3 for z.
= 4(24 – 32) + 42
= 4(16 – 9) + 16
Evaluate the exponent.
= 4(7) + 16
Subtract inside the parentheses. =
Multiply from left to right.
= 44
Add.

16. Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.
Check It Out: Example 3
Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.
z – 7(2x – xy)
Substitute 5 for x, 2 for y, and 60 for z.
= 60 – 7(25 – 52)
= 60 – 7(32 – 25)
Evaluate the exponent.
= 60 – 7(7)
Subtract inside the parentheses.
= 60 – 49
Multiply from left to right.
= 11
Subtract.

17. Additional Example 4: Geometry Application
1 2
Use the formula (n2 – 3n) to find the number of diagonals in a 7-sided figure.
(n2 – 3n) 1 2
(72 – 3 • 7) 1 2
Substitute the number of sides for n.
(49 – 3 • 7) 1 2
Evaluate the exponent.
(49 – 21) 1 2
Multiply inside the parentheses.
(28) 1 2
Subtract inside the parentheses.
14 diagonals
Multiply

18. Additional Example 4 Continued
A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals.

19. (n2 – 3n) (42 – 3 • 4) (16 – 3 • 4) (16 – 12) (4) 2 diagonals
Check It Out: Example 4
1 2
Use the formula (n2 – 3n) to find the number of diagonals in a 4-sided figure.
(n2 – 3n) 1 2
(42 – 3 • 4) 1 2
Substitute the number of sides for n.
(16 – 3 • 4) 1 2
Evaluate the exponents.
(16 – 12) 1 2
Multiply inside the parentheses.
(4) 1 2
Subtract inside the parentheses.
2 diagonals
Multiply.

20. Check It Out: Example 4 Continued
A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals.

21. Write in exponential form.
Lesson Quiz: Part I
Write in exponential form.
1. n • n • n • n 4 n
2. (–8) • (–8) • (–8) • (h)
(–8)3h
3. Evaluate (–4)4
256
4. Evaluate x • z – yx for x = 5, y = 3, and z = 6.
–213

22. Lesson Quiz: Part II
5. A population of bacteria doubles in size every minute. The number of bacteria after 5 minutes is 15  25. How many are there after 5 minutes?
480