Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Evaluate. 1. 103 1000 2. 101 1 3. 104 10,000 4. 105 100,000 5. 106 1,000,000

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

Sunshine State Standards Prep for MA.8.A.6.1 Use exponents…to write large and small numbers and vice versa and to solve problems. Also MA.8.A.6.4

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.

Additional Example 1: Using a Pattern to Simplify Negative Exponents Simplify. Write in decimal form. A. 10–2 10–2 = 1 10 • 10 Extend the pattern from the table. = 1 100 = 0.01 Multiply. Write as a decimal. B. 10–1 Extend the pattern from the table. = 1 10 = 0.1 Write as a decimal.

10–8 = Check It Out: Example 1A Simplify. Write in decimal form. 10–8 100,000,000 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 0.00000001 10–8

10–5 = Check It Out: Example 1B 10–5 10 • 10 • 10 • 10 • 10 1 100,000 = 0.00001 10–5

NEGATIVE EXPONENTS

Additional Example 2A: Evaluating Negative Exponents Simplify. 5–3 Write the power under 1; change the sign of the exponent. Find the product. Simplify.

Additional Example 2B: Evaluating Negative Exponents Simplify. (–10)–3 Write the power under 1; change the sign of the exponent. 1 –10 • –10 • –10 Find the product. –1000 1 = –0.001 Simplify.

(–3)5 1 Check It Out: Example 2A Simplify. (–3)–5 = or – –243 (–3) • (–3) • (–3) • (–3) • (–3) (–3)–5 243

(–4) • (–4) • (–4) • (–4) • (–4) • (–4) Check It Out: Example 2B Simplify. (–4)–6 4096 1 (–4)6 (–4) • (–4) • (–4) • (–4) • (–4) • (–4) (–4)–6 =

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 1 8 Evaluate the exponents. = 5 7 8 Add and subtract from left to right.

Check It Out: Example 3A Simplify 10 + (5 + 3)–2 + 50. + 10 + 8–2 + 1 = 11 1 82 = 11 + 1 64 = 11

Check It Out: Example 3B Simplify (7 – 3)3 + 2–2 – 5. 43 + 2–2 – 5 = 64 = 59 1 4 + 1 22 = 64 + – 5 = 59 +

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 18

Lesson Quiz Evaluate the powers of 10. 1. 10–3 0.001 2. 10–7 0.0000001 Evaluate. 1 36 3. (–6)–2 3 5 4. 4 • 2–3 +10–1 24 25 5. 80 –(11 – 24)–2 65 256 6. (4w)–2 + w–1 for w = 4

Lesson Quiz for Student Response Systems 1. Evaluate 10–4. A. –40 B. 0.001 C. 0.0001 D. 0.00001 20

Lesson Quiz for Student Response Systems 2. Evaluate 2–4. A. –8 B. 8 C. 16 D. 21

Lesson Quiz for Student Response Systems 3. Evaluate 82 –(11 – 20)–2. A. –8 B. 62 C. 64 D. 156 22