Course 3

4-1 Exponents4-1 Exponents

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Course 3

4-1 Exponents

Warm UpFind the product.

6251. 5 • 5 • 5 • 5

2. 3 • 3 • 3

3. (–7) • (–7) • (–7)

4. 9 • 9

27

–343

81

Course 3

4-1 Exponents

Problem of the Day

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

Course 3

4-1 Exponents

Learn to evaluate expressions with exponents.

Course 3

4-1 Exponents

Vocabulary

exponential form

exponent

base

power

Course 3

4-1 Exponents

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.

7

ExponentBase

2

Course 3

4-1 Exponents

Identify how many times 4 is a factor.4 • 4 • 4 • 4 = 44

Write in exponential form.

Additional Example 1: Writing Exponents

A. 4 • 4 • 4 • 4

Read –(63) as “6 to the 3rd power or 6 cubed”.

Reading Math

Identify how many times –6 is a factor.

(–6) • (–6) • (–6) = (–6)3

B. (–6) • (–6) • (–6)

Course 3

4-1 Exponents

Identify how many times 5 and d are used as a factor.

Additional Example 1: Writing Exponents

C. 5 • 5 • d • d • d • d

Write in exponential form.

5 • 5 = 52d4

Course 3

4-1 Exponents

Identify how many times x is a factor.x • x • x • x • x = x5

Write in exponential form.

Check It Out: Example 1

A. x • x • x • x • x

Identify how many times d is a factor.

d • d • d = d3

B. d • d • d

Course 3

4-1 Exponents

Identify how many times 7 and b are used as a factor.7 • 7 = 72 b2

Check it Out: Example 1

C. 7 • 7 • b • b

Write in exponential form.

Course 3

4-1 Exponents

A. 35

= 243

35 = 3 • 3 • 3 • 3 • 3Find the product of five 3’s.

= –243

= (–3) • (–3) • (–3) • (–3) • (–3)(–3)5

Find the product of five –3’s.B. (–3)5

Always use parentheses to raise a negative number to a power.

Helpful Hint

Evaluate.Additional Example 2: Evaluating Powers

Course 3

4-1 Exponents

D. 28

= 256

28 = 2 • 2 • 2 • 2 • 2 • 2 • 2 • 2

= 256

= (–4) • (–4) • (–4) • (–4) (–4)4

C. (–4)4

Evaluate.

Additional Example 2: Evaluating Powers

Find the product of four –4’s.

Find the product of eight 2’s.

Course 3

4-1 Exponents

A. 74

= 240174 = 7 • 7 • 7 • 7

Find the product of four 7’s.

= –729= (–9) • (–9) • (–9)(–9)3

Find the product of three –9’s.B. (–9)3

Evaluate.

Check It Out: Example 2

Course 3

4-1 Exponents

D. 97

= –25

97 = 9 • 9 • 9 • 9 • 9 • 9 • 9

= 4,782,969

= –(5) • (5) –(5)2

C. –(5)2

Evaluate.

Check It Out: Example 2

Find the product of two 5’s and then make the answer negative.

Find the product of seven 9’s.

Course 3

4-1 Exponents

Additional Example 3: Using the Order of Operations

= 4(7) + 16

Substitute 4 for x, 2 for y, and 3 for z.

Evaluate the exponent.

Subtract inside the parentheses.

Multiply from left to right.

= 4(24 – 32) + 42

= 4(16 – 9) + 16

= 28 + 16

Evaluate x(yx – zy) + x for x = 4, y = 2, and z = 3.

y

x(yx – zy) + x y

Add. = 44

Course 3

4-1 Exponents

Check It Out: Example 3

= 60 – 7(7)

Substitute 5 for x, 2 for y, and 60 for z.

Evaluate the exponent.

Subtract inside the parentheses.

Multiply from left to right.

= 60 – 7(25 – 52)

= 60 – 7(32 – 25)

= 60 – 49

Evaluate z – 7(2x – xy) for x = 5, y = 2, and z = 60.

z – 7(2x – xy)

Subtract. = 11

Course 3

4-1 Exponents

(72 – 3 • 7)1

2

Additional Example 4: Geometry Application

Evaluate the exponent.

Multiply inside the parentheses.

Multiply

Substitute the number of sides for n.

Subtract inside the parentheses.

14 diagonals

(49 – 21)1

2

(n2 – 3n)1

2

(49 – 3 • 7)1

2

(28)1

2

Use the formula (n2 – 3n) to find the number of diagonals in a 7-sided figure.

1 2

Course 3

4-1 Exponents

A 7-sided figure has 14 diagonals. You can verify your answer by sketching the diagonals.

Additional Example 4 Continued

Course 3

4-1 Exponents

(42 – 3 • 4)1

2

Check It Out: Example 4

Evaluate the exponents.

Multiply inside the parentheses.

Multiply

Substitute the number of sides for n.

Subtract inside the parentheses.

2 diagonals

(16 – 12)1

2

(n2 – 3n)1

2

(16 – 3 • 4)1

2

(4)1

2

Use the formula (n2 – 3n) to find the number of diagonals in a 4-sided figure.

1 2

Course 3

4-1 Exponents

A 4-sided figure has 2 diagonals. You can verify your answer by sketching the diagonals.

Check It Out: Example 4 Continued

Course 3

4-1 Exponents

Lesson Quiz: Part I

Write in exponential form.

1. n • n • n • n

2. (–8) • (–8) • (–8) • (h)

256

–213

(–8)3h

3. Evaluate (–4)4

4. Evaluate x • z – yx for x = 5, y = 3, and z = 6.

4n

Course 3

4-1 Exponents

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?

Lesson Quiz: Part II

480