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- 1. Evaluating Expressions and Properties
- 2. Evaluate expressions containing exponents. Objective
- 3. A power is an expression written with an exponent and a base or the value of such an expression. 3² is an example of a power. The base is the number that is used as a factor. The exponent, 2 tells how many times the base, 3, is used as a factor. 3 2
- 4. There are no easy geometric models for numbers raised to exponents greater than 3, but you can still write them using repeated multiplication or a base and exponent. 3 to the second power, or 3 squared 3 3 3 3 3 Multiplication Power Value Words 3 3 3 3 3 3 3 3 3 3 3 to the first power 3 to the third power, or 3 cubed 3 to the fourth power 3 to the fifth power 3 9 27 81 243 3 1 Reading Exponents 3 2 3 3 3 4 3 5
- 5. Caution! In the expression –5 2 , 5 is the base because the negative sign is not in parentheses. In the expression (–2), –2 is the base because of the parentheses.
- 6. Evaluate each expression. A. (–6) 3 (–6)(–6)(–6) – 216 B. –10 2 – 1 • 10 • 10 – 100 Use –6 as a factor 3 times. Find the product of –1 and two 10’s. Example 2: Evaluating Powers Think of a negative sign in front of a power as multiplying by a –1.
- 7. Evaluate each expression. a. (–5) 3 b. –6 2 Check It Out! Example 2 (–5)(–5)(–5) Use –5 as a factor 3 times. – 125 – 1 6 6 – 36 Think of a negative sign in front of a power as multiplying by –1. Find the product of –1 and two 6’s.
- 8. Use the order of operations to simplify expressions. Objective
- 9. When a numerical or algebraic expression contains more than one operation symbol, the order of operations tells which operation to perform first. First: Second: Third: Fourth: Perform operations inside grouping symbols. Evaluate powers. Perform multiplication and division from left to right. Perform addition and subtraction from left to right. Order of Operations
- 10. Grouping symbols include parentheses ( ), brackets [ ], and braces { }. If an expression contains more than one set of grouping symbols, evaluate the expression from the innermost set first.
- 11. Helpful Hint The first letter of these words can help you remember the order of operations. P lease E xcuse M y D ear A unt S ally P arentheses E xponents M ultiply D ivide A dd S ubtract
- 12. Simplify each expression. A. 15 – 2 · 3 + 1 15 – 2 · 3 + 1 15 – 6 + 1 10 There are no grouping symbols. Multiply. Subtract and add from left to right. B. 12 – 3 2 + 10 ÷ 2 12 – 3 2 + 10 ÷ 2 12 – 9 + 10 ÷ 2 12 – 9 + 5 8 There are no grouping symbols. Evaluate powers. The exponent applies only to the 3. Divide. Subtract and add from left to right. Example 1: Translating from Algebra to Words
- 13. 5.4 – 3 2 + 6.2 5.4 – 3 2 + 6.2 There are no grouping symbols. 5.4 – 9 + 6.2 Simplify powers. – 3.6 + 6.2 2.6 Subtract Add. Check It Out! Example 1b Simplify the expression.
- 14. Example 2A: Evaluating Algebraic Expressions Evaluate the expression for the given value of x. 10 – x · 6 for x = 3 10 – x · 6 10 – 3 · 6 10 – 18 – 8 First substitute 3 for x. Multiply. Subtract.
- 15. Evaluate the expression for the given value of x. 4 2 ( x + 3) for x = –2 4 2 ( x + 3) 4 2 ( –2 + 3) 4 2 ( 1 ) 16 (1) 16 First substitute –2 for x. Perform the operation inside the parentheses. Evaluate powers. Multiply. Example 2B: Evaluating Algebraic Expressions
- 16. Fraction bars, radical symbols, and absolute-value symbols can also be used as grouping symbols. Remember that a fraction bar indicates division.
- 17. Check It Out! Example 3a Simplify. 5 + 2(–8) (–2) – 3 3 1 The fraction bar acts as a grouping symbol. Simplify the numerator and the denominator before dividing. Evaluate the power in the denominator. Multiply to simplify the numerator. Add. Divide. 5 + 2(–8) – 8 – 3 5 + 2(–8) (–2) – 3 3 5 + ( –16 ) – 8 – 3 – 11 – 11
- 18. Identify the Commutative, Associative, and Distributive Properties to simplify expressions. Objectives
- 20. The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

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