2-6 Exponents

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm UpFind the product.

Course 3

2-6 Exponents

6251. 5 • 5 • 5 • 5

2. 3 • 3 • 3

3. (–7) • (–7) • (–7)

4. 9 • 9

27

–343

81

Problem of the Day

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

Course 3

2-6 Exponents

2 and 2

Learn to evaluate expressions with exponents.

Course 3

2-6 Exponents

Course 3

2-6 Exponents

Vocabulary

power

exponential form

exponent

base

The term 27 is called a power. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor.

Course 3

2-6 Exponents

7

ExponentBase

2

Course 3

2-6 Exponents

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

Write in exponential form.

Additional Example 1A & 1B: Writing Exponents

A. 4 • 4 • 4 • 4

Identify how many times d is a factor.

d • d • d • d • d = d5

B. d • d • d • d • d

Read 44 as “4 to the 4th power.”Reading Math

Course 3

2-6 Exponents

Identify how many times –6 is a factor.

(–6) • (–6) • (–6) = (–6)3

Identify how many times 5 is a factor.5 • 5 = 52

Additional Example 1C & 1D: Writing Exponents

C. (–6) • (–6) • (–6)

D. 5 • 5

Write in exponential form.

Course 3

2-6 Exponents

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

Write in exponential form.

Try This: Example 1A & 1B

A. x • x • x • x • x

Identify how many times d is a factor.

d • d • d = d3

B. d • d • d

Course 3

2-6 Exponents

Identify how many times –3 is a factor.

(–3) • (–3) • (–3) • (–3) = (–3)4

Identify how many times 7 is a factor.7 • 7 = 72

Try This: Example 1C & 1D

C. (–3) • (–3) • (–3) • (–3)

D. 7 • 7

Write in exponential form.

Course 3

2-6 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 2A & 2B: Evaluating Powers

Course 3

2-6 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 2C & 2D: Evaluating Powers Continued

Find the product of four –4’s.

Find the product of eight 2’s.

Course 3

2-6 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.

Try This: Example 2A & 2B

Course 3

2-6 Exponents

D. 97

= 25

97 = 9 • 9 • 9 • 9 • 9 • 9 • 9

= 4,782,969

= (–5) • (–5)(–5)2

C. (–5)2

Evaluate.

Try This: Example 2C & 2D

Find the product of two –5’s.

Find the product of seven 9’s.

Additional Example 3: Simplifying Expressions Containing Powers

Course 3

2-6 Exponents

= 47

Simplify (25 – 32) + 6(4).

= (32 – 9) + 6(4)

= (23) + 6(4)

= 23 + 24

Evaluate the exponents.

Subtract inside the parentheses.

Multiply from left to right.

Add from left to right.

Course 3

2-6 Exponents

Try This: Example 3

= –49

Simplify (32 – 82) + 2 • 3.

= (9 – 64) + 2 • 3

= (–55) + 2 • 3

= –55 + 6

Evaluate the exponents.

Subtract inside the parentheses.

Multiply from left to right.

Add from left to right.

(72 – 3 • 7)1

2

Additional Example 4: Geometry Application

Course 3

2-6 Exponents

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

2-6 Exponents

Verify your answer by sketching the diagonals.

14 Diagonals

Additional Example 4 Continued

(42 – 3 • 4)1

2

Try This: Example 4

Course 3

2-6 Exponents

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

2-6 Exponents

Verify your answer by sketching the diagonals.

2 diagonals

Try This: Example 4 Continued

Course 3

2-6 Exponents

Lesson Quiz: Part 1

Write in exponential form.

1. n • n • n • n

2. (–8) • (–8) • (–8)

256

3

(–8)3

3. Evaluate (–4)4

4. Simplify 99 – 3(4 • 23).

4n

Course 3

2-6 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 2

480