4-2 Warm Up Problem of the Day Lesson Presentation Look for a Pattern in Integer Exponents Course 3 Warm Up Problem of the Day Lesson Presentation

Warm Up Evaluate. 1. 103 1000 2. 100 1 3. 102 • 102 10,000 107 104 4. 1000 106 5. 1

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

Learn to evaluate expressions with negative exponents and to evaluate the zero exponent.

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.

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

Extend the pattern from the table. Check It Out: Example 1A Evaluate the powers of 10. 10–8 Extend the pattern from the table. 10–8 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 Multiply. 10–8 = 1 100,000,000 Write as a decimal. = 0.00000001

Extend the pattern from example 1A. Check It Out: Example 1B 10–9 Extend the pattern from example 1A. 10–9 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 Multiply. 10–9 = 1 1,000,000,000 Write as a decimal. = 0.000000001

NEGATIVE EXPONENTS Remember! The reciprocal of a number is 1 divided by that number. Remember!

Additional Example 2A: Evaluating Negative Exponents Evaluate. 5–3 5 1 3 = Write the reciprocal; change the sign of the exponent. 1 5 • 5 • 5 = Find the product of three ’s. 1 5 125 1 = Simplify.

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

Evaluate. 4–2 1 4 Check It Out: Example 2A = Write the reciprocal; change the sign of the exponent. 1 4 • 4 = Find the product of two ’s. 1 4 16 1 = Simplify.

Evaluate. (–7)–4 Check It Out: Example 2B 1 = –7 4 Write the reciprocal; change the sign of the exponent. 1 –7 • –7 • –7 • –7 = Find the product of four ’s. 1 –7 2401 1 = Simplify.

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 3 Evaluate 3 + (7 – 4)–2 + (–8)0. 3 + (7 – 4)–2 + (–8)0 = 3 + (3)–2 + (–8)0 Subtract inside the parentheses. = 3 + + 1 1 9 Evaluate the exponents. = 4 1 9 Add.

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