Evaluating Algebraic Expressions

4-2 Integer Exponents

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Evaluating Algebraic Expressions

4-2 Integer Exponents

105

Warm UpSimplify.

10001. 103

2. 101

3. 104

10

10,000

100,0004.

5. 106 1,000,000

Evaluating Algebraic Expressions

4-2 Integer Exponents

NS2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base.AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents.

California Standards

Evaluating Algebraic Expressions

4-2 Integer Exponents

Look at the pattern shown in the table to extend what you know about exponents to include negative exponents.

÷ 10 ÷ 10 ÷ 10 ÷ 10

102 101 100 10–1 10–2

10 • 10

100

10

10 1

1 110

110

= 0.1

110 • 10

1100

= 0.01

Evaluating Algebraic Expressions

4-2 Integer Exponents

Notice from the chart that as the exponents decrease by 1, the value of the expression decreases by a factor of 10.

÷ 10 ÷ 10 ÷ 10 ÷ 10

102 101 100 10–1 10–2

10 • 10

100

10

10 1

1 110

110

= 0.1

110 • 10

1100

= 0.01

Evaluating Algebraic Expressions

4-2 Integer ExponentsAdditional Example 1: Using a Pattern to Evaluate

Negative ExponentsSimplify the powers of 10.

A. 10–2

10–2 = 1

10 • 10

= 1100

= 0.01

B. 10–1

= = 0.1 110

10 =

–1 110

Multiply. Write as a decimal.

Multiply. Write as a decimal.

Evaluating Algebraic Expressions

4-2 Integer ExponentsCheck It Out! Example 1A

Simplify the powers of 10.

10–8

=1

100,000,000

10–8 = 1

10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

Extend the pattern from the table.

= 0.00000001

Multiply.

Write as a decimal.

Evaluating Algebraic Expressions

4-2 Integer ExponentsCheck It Out! Example 1B

10–9

= 11,000,000,000

10–9 =1

10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10

Extend the pattern from Example 1A.

= 0.000000001

Multiply.

Write as a decimal.

Simplify the powers of 10.

Evaluating Algebraic Expressions

4-2 Integer Exponents

NEGATIVE EXPONENTS

Evaluating Algebraic Expressions

4-2 Integer Exponents

5–3

Write the power under 1; change the sign of the exponent.

Additional Example 2A: Evaluating Negative Exponents

Simplify.

Find the product.

Simplify.

15 • 5 • 5

=

1251

=

Evaluating Algebraic Expressions

4-2 Integer Exponents

(–10)–3

Write the power under 1; change the sign of the exponent.

Additional Example 2B: Evaluating Negative Exponents

Simplify.

Find the product.

Simplify.

1–10 • –10 • –10

=

–1000 1

= = –0.001

Evaluating Algebraic Expressions

4-2 Integer Exponents

4–2

Write the power under 1; change the sign of the exponent.

Check It Out! Example 2A

Simplify.

Find the product.

Simplify.

14 • 4

=

161

=

Evaluating Algebraic Expressions

4-2 Integer Exponents

(–7)–4

Write the power under 1; change the sign of the exponent.

Check It Out! Example 2B

Simplify.

Find the product.

Simplify.

1

–7 • –7 • –7 • –7 =

2401 1

=

Evaluating Algebraic Expressions

4-2 Integer Exponents

Evaluating Algebraic Expressions

4-2 Integer Exponents

Subtract inside the parentheses.

Simplify 5 – (6 – 4)–3 + (–2)0.

Rewrite 2-3.

Additional Example 3: Using the Order of Operations

5 – (6 – 4)–3 + (–2)0

5 – (2)–3 + (–2)0

5 7 8

Add and subtract from left to right.

5 – + 1 1 23

Simplify the powers. 5 – + 1 1 8

Evaluating Algebraic Expressions

4-2 Integer Exponents

Subtract inside the parentheses.

Simplify 3 + (7 – 4)–2 + (–8)0.

Rewrite 3-2.

Check It Out! Example 3

3 + (7 – 4)–2 + (–8)0

3 + (3)–2 + (–8)0

Simplify the powers.

4 1 9

3 + + 1 1 9

3 + + (–8)0 1 32

Add.

Evaluating Algebraic Expressions

4-2 Integer ExponentsLesson Quiz

Simplify the powers of 10.

1. 10–3 0.001

2. 10–7 0.0000001

Simplify.

3. (–6)–2

4. 4 • 2–3 +10–1

5. 80 –(11 – 24)–2

1 36 3

524

256. Evaluate (4w)–2 + w–1 for w = 4.

65 256