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Look for Pattern Look for a a Pattern in 4-2 inInteger Exponents 4-2 Integer Exponents Warm Up Problem of the Day Lesson Presentation Course Course 3 3 Look for a Pattern 4-2 in Integer Exponents Warm Up Evaluate. 1. 103 1000 2. 100 1 3. 102 • 102 10,000 4. 107 1000 104 5. 106 1 106 Course 3 Look for a Pattern 4-2 in Integer Exponents 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 Course 3 Look for a Pattern 4-2 in Integer Exponents Learn to evaluate expressions with negative exponents and to evaluate the zero exponent. Course 3 Look for a Pattern 4-2 in Integer Exponents –2 10 2 101 100 10–1 10 10 • 10 10 1 1 1 10 10 • 10 1 = 0.1 1 = 0.01 100 10 1 10 100 ÷ 10 ÷ 10 ÷ 10 ÷ 10 Look for a pattern in the table to extend what you know about exponents to include negative exponents. Course 3 Look for a Pattern 4-2 in Integer Exponents Additional Example 1A & 1B: Using a Pattern to Evaluate Negative Exponents Evaluate the powers of 10. A. 10–2 1 Extend the pattern 10–2 = 10 • 10 from the table. 1 Multiply. Write as a 10–2 = = 0.01 100 decimal. B. 10–1 1 Extend the pattern 10 –1 = from the table. 10 10 –1 = 1 = 0.1 Multiply. Write as a 10 decimal. Course 3 Look for a Pattern 4-2 in Integer Exponents Check It Out: Example 1A Evaluate the powers of 10. 10–8 Extend the pattern from the table. 1 10–8 = 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 Multiply. 1 10–8 = 100,000,000 Write as a decimal. = 0.00000001 Course 3 Look for a Pattern 4-2 in Integer Exponents Check It Out: Example 1B 10–9 Extend the pattern from example 1A. 1 10–9 = 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 Multiply. 1 10–9 = 1,000,000,000 Write as a decimal. = 0.000000001 Course 3 Look for a Pattern 4-2 in Integer Exponents NEGATIVE EXPONENTS Remember! The reciprocal of a number is 1 divided by that number. Course 3 Look for a Pattern 4-2 in Integer Exponents Additional Example 2A: Evaluating Negative Exponents Evaluate. 5–3 3 Write the reciprocal; change the = 1 5 sign of the exponent. = 1 Find the product of three 1 ’s. 5•5•5 5 1 Simplify. = 125 Course 3 Look for a Pattern 4-2 in Integer Exponents Additional Example 2B: Evaluating Negative Exponents Evaluate. (–10)–3 1 3 Write the reciprocal; change = –10 the sign of the exponent. 1 1 ’s. = Find the product of three –10 • –10 • –10 –10 1 = = –0.001 Simplify. –1000 Course 3 Look for a Pattern 4-2 in Integer Exponents Check It Out: Example 2A Evaluate. 4–2 2 Write the reciprocal; change the = 1 4 sign of the exponent. = 1 Find the product of two 1 ’s. 4•4 4 1 Simplify. = 16 Course 3 Look for a Pattern 4-2 in Integer Exponents Check It Out: Example 2B Evaluate. (–7)–4 1 4 Write the reciprocal; change = –7 the sign of the exponent. = 1 Find the product of four 1 ’s. –7 • –7 • –7 • –7 –7 1 = Simplify. 2401 Course 3 Look for a Pattern 4-2 in Integer Exponents Course 3 Look for a Pattern 4-2 in Integer Exponents 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 Evaluate the exponents. 8 = 57 Add and subtract from left to 8 right. Course 3 Look for a Pattern 4-2 in Integer Exponents 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 Evaluate the exponents. 9 =41 Add. 9 Course 3 Look for a Pattern 4-2 in Integer Exponents Lesson Quiz Evaluate the powers of 10. 1. 10–3 0.001 2. 10–7 0.0000001 Evaluate. 1 3. (–6)–2 36 3 4. 4 • 2–3 + 10–1 5 24 5. 80 – (11 – 24)–2 25 65 6. (4w)–2 + w–1 for w = 4 256 Course 3