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

Course Look for a Pattern in Integer Exponents Warm Up Evaluate ,

Course Look for a Pattern in Integer Exponents Learn to evaluate expressions with negative exponents and to evaluate the zero exponent.

Course Look for a Pattern in Integer Exponents Look for a pattern in the table to extend what you know about exponents to include negative exponents. ÷ –1 10 – = = 0.01

Course Look for a Pattern in Integer Exponents Example 1: Using a Pattern to Evaluate Negative Exponents Evaluate the powers of 10. A. 10 –2 10 –2 = –2 = = 0.01 B. 10 –1 10 = = 0.1 – = – Extend the pattern from the table. Multiply. Write as a decimal. Extend the pattern from the table. Multiply. Write as a decimal.

Course Look for a Pattern in Integer Exponents Check It Out: 1A Evaluate the powers of –8 10 –8 = 1 100,000, –8 = Extend the pattern from the table. = Multiply. Write as a decimal.

Course Look for a Pattern in Integer Exponents Check It Out 10 –9 10 –9 = 1 1,000,000, –9 = Extend the pattern from example 1A. = Multiply. Write as a decimal.

Course Look for a Pattern in Integer Exponents NEGATIVE EXPONENTS The reciprocal of a number is 1 divided by that number. Remember!

Course Look for a Pattern in Integer Exponents 5 –3 Write the reciprocal; change the sign of the exponent. Example 2: Evaluating Negative Exponents Evaluate. Find the product of three ’s Simplify = = =

Course Look for a Pattern in Integer Exponents 4 –2 Write the reciprocal; change the sign of the exponent. Check It Out: 2A Evaluate. Find the product of two ’s Simplify = 1 4 = 16 1 =

Course Look for a Pattern in Integer Exponents (–10) –3 Write the reciprocal; change the sign of the exponent. Example 3: Evaluating Negative Exponents Evaluate. Find the product of three ’s. 1 –10 Simplify. 1 = – –10 –10 –10 = – = = –0.001

Course Look for a Pattern in Integer Exponents (–7) –4 Write the reciprocal; change the sign of the exponent. Check It Out: 3A Evaluate. Find the product of four ’s. 1 –7 Simplify. 1 = –7 4 1 –7 –7 = =

Course Look for a Pattern in Integer Exponents

Course Look for a Pattern in Integer Exponents Subtract inside the parentheses. Evaluate 5 – (6 – 4) –3 + (– 2) 0. Evaluate the exponents. Example 4: Using the Order of Operations 5 – (6 – 4) –3 + (–2) 0 = 5 – (2) –3 + (–2) 0 = 5 – = Add and subtract from left to right.

Course Look for a Pattern in Integer Exponents Subtract inside the parentheses. Evaluate 3 + (7 – 4) –2 + (–8) 0. Evaluate the exponents. Check It Out: 4A 3 + (7 – 4) –2 + (–8) 0 = 3 + (3) –2 + (–8) 0 = = Add.

Course Look for a Pattern in Integer Exponents Lesson Quiz Evaluate the powers of – – Evaluate. 3. (–6) – –3 +10 – –(11 – 2 4 ) – (4w) –2 + w –1 for w =