7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. ANSWER: a 3 b 2 c 9.
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1 2. Simplify each expression. Assume that no denominator equals zero. a 3 b 2 c 9 4. c 3 f 3 6. r nq 2 w rt 2 esolutions Manual - Powered by Cognero Page 1
2 FINANCIAL LITERACY The gross domestic product (GDP) for the United States in 2008 was $ trillion, and the GDP per person was $47,580. Use order of magnitude to approximate the population of the United States in or 100,000,000 Simplify each expression. Assume that no denominator equals zero. p 10 t c esolutions Manual - Powered by Cognero Page 2
3 p 10 r a 4 b 16 c g 5 h 7 esolutions Manual - Powered by Cognero Page 3
4 44. PROBABILITY The probability of rolling a die and getting an even number is. If you roll the die twice, the probability of getting an even number twice is or. a. What does represent? b. Write an expression to represent the probability of rolling a die d times and getting an even number every time. Write the expression as a power of 2. a. probability of all evens on 4 rolls b. ; 2 d 46. Simplify each expression. Assume that no denominator equals zero esolutions Manual - Powered by Cognero Page 4
5 ASTRONOMY The brightness of a star is measured in magnitudes. The lower the magnitude, the brighter the star. A magnitude 9 star is 2.51 times as bright as a magnitude 10 star. A magnitude 8 star is or times as bright as a magnitude 10 star. a. How many times as bright is a magnitude 3 star as a magnitude 10 star? b. Write an expression to compare a magnitude m star to a magnitude 10 star. c. A full moon is considered to be approximately magnitude 13. Does your expression make sense for this magnitude? Explain. a or b m c. Sample answer: Yes; according to the expression, a full Moon would be or 1,557,742,231 times as bright as a magnitude 10 star. Since we know that the lower the magnitude the brighter the object, it follows that a magnitude -13 object is significantly brighter than a magnitude 10 object. esolutions Manual - Powered by Cognero Page 5
6 60. MULTIPLE REPRESENTATIONS To find the area of a circle, use A = πr 2. The formula for the area of a square is A = s 2. a. ALGEBRAIC Find the ratio of the area of the circle to the area of the square. b. ALGEBRAIC If the radius of the circle and the length of each side of the square is doubled, find the ratio of the area of the circle to the square. c. TABULAR Copy and complete the table. d. ANALYTICAL What conclusion can be drawn from this? a. b. c. d. The ratio of the area of the circle to the area of the square will always be. 62. OPEN ENDED Name two monomials with a quotient of 24a 2 b 3. Sample answer: 24a 4 b 6 and a 2 b 3 esolutions Manual - Powered by Cognero Page 6
7 64. CCSS REGULARITY Write a convincing argument to show why 3 0 = 1. We can use the Quotient of Powers Property to show that 3 0 = What is the perimeter of the figure in meters? A 40x B 80x C 160x D 400x B 68. EXTENDED RESPONSE Jessie and Jonas are playing a game using the spinners shown. Each spinner is equally likely to stop on any of the four numbers. In the game, a player spins both spinners and calculates the product of the two numbers on which the spinners have stopped. a. What product has the greatest probability of occurring? b. What is the probability of that product occurring? a. 4 b. esolutions Manual - Powered by Cognero Page 7
8 70. GEOMETRY A rectangular prism has a width of 7x 3 units. a length of 4x 2 units, and a height of 3x units. What is the volume of the prism? 84x 6 units Solve each system of inequalities by graphing. 72. y 3 y x < y 2x < 2 y 2x > 4 no solution Solve each inequality. Check your solution (b 8) + 10 b t 3(t + 4) + 2 t (b + 5) > 3(b 5) esolutions Manual - Powered by Cognero Page 8
9 Evaluate each expression ,000, esolutions Manual - Powered by Cognero Page 9
7-2 Division Properties of Exponents. Simplify each expression. Assume that no denominator equals zero. SOLUTION: SOLUTION: SOLUTION: SOLUTION:
Simplify each expression. Assume that no denominator equals zero. 1. 2. 3. 4. Page 1 4. 5. 6. 7. Page 2 7. 8. 9. 10. Page 3 10. 11. 12. A value to the zero power is 1. 13. A value to the zero power is
Study Guide and Review - Chapter 6. Choose a word or term that best completes each statement.
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Find the value of c that makes each trinomial a perfect square. 1. x 2 18x + c 81 3. x 2 + 9x + c Solve each equation by completing the square. Round to the nearest tenth if necessary. 5. x 2 + 4x = 6
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Identify the domain and range of each function. 7. 1. 3. Graph each function. State the domain and range. 5. Graph each inequality. 9. esolutions Manual - Powered by Cognero Page 1 11. Graph each function.
Each element of the domain is paired with exactly one element of the range. So, the relation is a function.
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Simplify each expression. 1. 2. 3. MULTIPLE CHOICE Identify all values of x for which is undefined. A 7, 4 B 7, 4 C 4, 7, 7 D 4, 7 D Simplify each expression. 4. esolutions Manual - Powered by Cognero
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