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Evaluating Algebraic Expressions 4-2 Integer Exponents Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

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Evaluating Algebraic Expressions 4-2 Integer Exponents 10 5 Warm Up Simplify , , ,000,000

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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

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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. ÷ –1 10 – = = 0.01

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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. ÷ –1 10 – = = 0.01

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Evaluating Algebraic Expressions 4-2 Integer Exponents Additional Example 1: Using a Pattern to Evaluate Negative Exponents Simplify the powers of 10. A. 10 –2 10 –2 = 1 10 = = 0.01 B. 10 –1 = = = – Multiply. Write as a decimal.

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Evaluating Algebraic Expressions 4-2 Integer Exponents Check It Out! Example 1A Simplify the powers of –8 = 1 100,000, –8 = Extend the pattern from the table. = Multiply. Write as a decimal.

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Evaluating Algebraic Expressions 4-2 Integer Exponents Check It Out! Example 1B 10 –9 = 1 1,000,000, –9 = Extend the pattern from Example 1A. = Multiply. Write as a decimal. Simplify the powers of 10.

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Evaluating Algebraic Expressions 4-2 Integer Exponents NEGATIVE EXPONENTS

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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 = =

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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 = – = = –0.001

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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. 1 4 = 16 1 =

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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 = =

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Evaluating Algebraic Expressions 4-2 Integer Exponents

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Evaluating Algebraic Expressions 4-2 Integer Exponents Subtract inside the parentheses. Simplify 5 – (6 – 4) –3 + (–2) 0. Rewrite Additional Example 3: Using the Order of Operations 5 – (6 – 4) –3 + (–2) 0 5 – (2) –3 + (–2) Add and subtract from left to right. 5 – Simplify the powers. 5 –

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Evaluating Algebraic Expressions 4-2 Integer Exponents Subtract inside the parentheses. Simplify 3 + (7 – 4) –2 + (–8) 0. Rewrite Check It Out! Example (7 – 4) –2 + (–8) (3) –2 + (–8) 0 Simplify the powers (–8) Add.

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Evaluating Algebraic Expressions 4-2 Integer Exponents Lesson Quiz Simplify the powers of – – Simplify. 3. (–6) – –3 +10 – –(11 – 2 4 ) – Evaluate (4w) –2 + w –1 for w =

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