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Lesson Menu Five-Minute Check (over Chapter 8) Then/Now New Vocabulary Example 1: Write Expressions Using Exponents Example 2: Write Expressions Using Exponents Concept Summary: Order of Operations Example 3: Real-World Example: Evaluate Expressions Example 4: Evaluate Algebraic Expressions

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Over Chapter 8 5-Minute Check 1 A.Yes; there are 4 points. B.Yes; the y-values are different. C.No; 0 is paired with –1 and 2. D.No; there are not enough points. Determine whether the relation {(–2, –2), (0, –1), (–2, 1), (0, 2)} is a function.

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Over Chapter 8 5-Minute Check 2 A.x-int = 3; y-int = 3 B.x-int = 3; y-int = 6 C.x-int = 2; y-int = 6 D.x-int = 2; y-int = 3 Find the x-intercept and y-intercept for the graph 2x + y = 6.

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Over Chapter 8 5-Minute Check 3 Find the slope of the line that passes through the pair of points A(4, 2) and B(–4, –4). A. B. C. D.

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Over Chapter 8 5-Minute Check 4 State the slope and y-intercept for the graph of the equation x + 2y = –8. A. B. C. D.

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Over Chapter 8 5-Minute Check 5 A.r = 2s, r = s – 17 B.s = 2r, s = r + 17 C.r = 2s, r = s + 17 D.s = 2r, s = r – 17 Sarah collected twice as many canned goods for the food bank as Ryan. Ryan collected 17 cans less than Sarah. Which system of equations can be used to find the number of canned goods each friend collected?

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Then/Now You evaluated expressions without exponents. (Lesson 2–4) Write expressions using exponents. Evaluate expressions containing exponents.

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Vocabulary exponent power base

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Example 1 Write Expressions Using Exponents A. Write 9 9 9 9 using exponents. The base 9 is a factor 4 times. So, the exponent is 4. Answer: 9 9 9 9 = 9 4

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Example 1 Write Expressions Using Exponents B. Write (–1)(–1) using exponents. The base –1 is a factor 2 times. So, the exponent is 2. Answer: (–1) (–1) = (–1) 2

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Example 1 CYP A A.8 8 B.5 8 C.4 8 D.8 5 A. Which expression is the same as 8 8 8 8 8?

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Example 1 CYP B A.(–2) 3 B.2 8 C.(–3) 2 D.(3) –2 B. Which expression is the same as (–2)(–2)(–2)?

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Example 2 A Write Expressions Using Exponents A. Write w w w w w using exponents. The base w is a factor 5 times. So, the exponent is 5. Answer: w w w w w = w 5

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Example 2 B Write Expressions Using Exponents B. Write (5x + 1)(5x + 1) using exponents. Answer: (5x + 1)(5x + 1) = (5x + 1) 2 The base is 5x + 1. It is a factor 2 times, so the exponent is 2.

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Example 2 C Write Expressions Using Exponents First, group the factors with like bases. Then write using exponents. C. Write using exponents. Answer: x x x x = x 4 and y y y = y 3

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Example 2 CYP A A.b b B.–4 b C.4 b D.b 4 A. Which expression is the same as b b b b?

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Example 2 CYP B A.(4 – 2x) 2 B.4 – 2x 2 C.2(4 – 2x) D.4 2 – 2x 2 B. Write the expression using exponents. (4 – 2x)(4 – 2x)

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Example 2 CYP C A.9ab 5 B.9a 3 b 5 C.(9ab) 8 D.9a 8 b 8 C. Write the expression using exponents. 9 a a a b b b b b.

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Concept

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Example 3 Evaluate Expressions A. HOCKEY North American hockey rinks are built according to National Hockey League specifications. The distance from the goal line to the closest blue line is 2 6 feet. Evaluate the expression to find this dimension. 2 6 = 2 2 2 2 2 2 2 is a factor 6 times. = 64Simplify. Answer: The distance from the goal line to the closest blue line is 64 feet.

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Example 3 Evaluate Expressions B. HOCKEY North American hockey rinks are built according to National Hockey League specifications. The length of the rink is 2 3 5 2 feet. Evaluate the expression to find this dimension. 2 3 5 2 = 2 2 2 5 5 Evaluate powers. = 200Simplify. Answer: The length of the rink is 200 feet.

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Example 3 CYP A A.7 ft B.12 ft C.64 ft D.81 ft A. The distance between two houses is 4 3 feet. Evaluate 4 3 to find the distance.

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Example 3 CYP B A.135 ft B.150 ft C.1125 ft D.1250 ft B. The distance from the parking lot to the front door is 3 2 5 3 feet. Evaluate 3 2 5 3 to find the distance.

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Example 4 Evaluate Algebraic Expressions Evaluate x 2 – y 3 if x = –5 and y = 2. x 2 – y 3 = (–5) 2 – 2 3 Replace x with –5 and y with 2. = 25 – 8Evaluate powers; (–5) 2 = 25 and 2 3 = 8. = 17Subtract. Answer: 17

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Example 4 A.11 B.15 C.121 D.129 Evaluate x 3 – y 2 if x = 5 and y = –2.

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End of the Lesson

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