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Learning Task 1 Simplify by writing in exponential form 1. 2(2)(2)(2)(2)(2) Write in expanded form 26 (2x) = (2x)(2x)(2x)(2x) 2. (3a)(3a)(3a)(3a) (xy)7 = %3D 3. (-4)(-4)(-4)(-4)(-4) = (-ab)6 = %3D Exponents have its own rule in performing mathematical operations. The Laws of Exponents

Learning Task 1 Simplify by writing in exponential form 1. 2(2)(2)(2)(2)(2) Write in expanded form 26 (2x) = (2x)(2x)(2x)(2x) 2. (3a)(3a)(3a)(3a) (xy)7 = %3D 3. (-4)(-4)(-4)(-4)(-4) = (-ab)6 = %3D Exponents have its own rule in performing mathematical operations. The Laws of Exponents

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
ChapterP: Prerequisites
SectionP.5: Algebraic Expressions
Problem 90E: Building Envelope The building code in a certain town requires that a house be at least 10 ft from...
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Laws of Exponents and Its Application WEEK I Lesson 5 In the process of multiplication and division of polynomials you need to apply the laws of exponents. Remember that exponent tells how many times the base will be multiplied by itself. Any number an, a is the base and n is the exponent. 53 means 5-5 125 XHx XXx , the variable x is multiplied by it self 5 times, hence you can write it as x5. Here, the base is x and the exponent is 5 D Learning Task 1 Simplify by writing in exponential form Write in expanded form 1. 2(2)(2)(2)(2)(2) 26 %3D (2x) = (2x)(2x)(2x)(2x) 2. (3a)(3a)(3a)(3a) = (xy)7 = 3. (-4)(-4)(-4)(-4)(-4) = (-ab)6 = Exponents have its own rule in performing mathematical operations. The Laws of Exponents 1. Product Law of Exponent. Any numbers m and integers x and y, m* -m = m*+y The base must be the same before you can add the exponents. Example: b-b (b-b)(b.b.b) = b Similarly: b2.63 =62+3 =b% 2 Quotient Law of Exponents Any numbers m and integers x and y, m* =m* =1, if x = y m* 1 m*, if x > y if x < y a m m m Examples: a5 a a a aa a5 a. a = a a a = a3 similarly = a3 a3 b. a3 a a a Any number raised to zero = a3-3 = a0 = 1 =1 similarly a3 is always equal to 1 a a a a? a a a2 1 similarifu a+ a2 a? D.v. v.D 18
Transcribed Image Text:Laws of Exponents and Its Application WEEK I Lesson 5 In the process of multiplication and division of polynomials you need to apply the laws of exponents. Remember that exponent tells how many times the base will be multiplied by itself. Any number an, a is the base and n is the exponent. 53 means 5-5 125 XHx XXx , the variable x is multiplied by it self 5 times, hence you can write it as x5. Here, the base is x and the exponent is 5 D Learning Task 1 Simplify by writing in exponential form Write in expanded form 1. 2(2)(2)(2)(2)(2) 26 %3D (2x) = (2x)(2x)(2x)(2x) 2. (3a)(3a)(3a)(3a) = (xy)7 = 3. (-4)(-4)(-4)(-4)(-4) = (-ab)6 = Exponents have its own rule in performing mathematical operations. The Laws of Exponents 1. Product Law of Exponent. Any numbers m and integers x and y, m* -m = m*+y The base must be the same before you can add the exponents. Example: b-b (b-b)(b.b.b) = b Similarly: b2.63 =62+3 =b% 2 Quotient Law of Exponents Any numbers m and integers x and y, m* =m* =1, if x = y m* 1 m*, if x > y if x < y a m m m Examples: a5 a a a aa a5 a. a = a a a = a3 similarly = a3 a3 b. a3 a a a Any number raised to zero = a3-3 = a0 = 1 =1 similarly a3 is always equal to 1 a a a a? a a a2 1 similarifu a+ a2 a? D.v. v.D 18
Subtract. 43 cannot be divided by x. Hence 43 1s the re- 43 mainder 20x -40 43 The quotient is 6x2 + 9x + 20 R. 43 or 6x2 + 9x + 20 + 21 E Learning Task 2: A. Simplify B. Perform the indicated operations. Simplify your answer 1. (-m4)3 7. 16a b'c'-24a'he +44a'b'c 4a bc 1. 2ab( 4a2 + 3ab 7b2) .arm 2 10c 2. -3xy(x³y3 - 3x2y + 7xy2) 2. 2d3 30c? +19ac-63a? 8. 3. (x+ 2)(x2 -3x + 2) 6c-7a 3. (3a?bc)3 4. (2x 1)(2x2 + 4x + 3) 4. (2x3y2z)(3x?yz?) 5. (12y2 -9y + 16)(8y3 -14y + 5) 9. (a6 + b6) (a2 + 6. 25a b'c 3m2n 5. 6w +7w? -12w +15 10. 5ab*c xy? 2 2mn 2w2 +3w-5 S obiviaI :olqs Learning Task 3: Solve. 1. What is the area of the rectangle whose length is (x + 5) and width (x 5)? 2. What is the area of the square whose sides measure (3x + 4)? 3. The area of the rectangle is 3x2 + 7x - 6, what is the length if the width is (x +3) 4. What is the average speed of the car that covers a distance of (2y3-7y2 + 5y - 1) km in (2y-1) hour? olum 5. Multiply (m2 + 2m-2) by the sum of (m + 3 iand (2m - 3)
Transcribed Image Text:Subtract. 43 cannot be divided by x. Hence 43 1s the re- 43 mainder 20x -40 43 The quotient is 6x2 + 9x + 20 R. 43 or 6x2 + 9x + 20 + 21 E Learning Task 2: A. Simplify B. Perform the indicated operations. Simplify your answer 1. (-m4)3 7. 16a b'c'-24a'he +44a'b'c 4a bc 1. 2ab( 4a2 + 3ab 7b2) .arm 2 10c 2. -3xy(x³y3 - 3x2y + 7xy2) 2. 2d3 30c? +19ac-63a? 8. 3. (x+ 2)(x2 -3x + 2) 6c-7a 3. (3a?bc)3 4. (2x 1)(2x2 + 4x + 3) 4. (2x3y2z)(3x?yz?) 5. (12y2 -9y + 16)(8y3 -14y + 5) 9. (a6 + b6) (a2 + 6. 25a b'c 3m2n 5. 6w +7w? -12w +15 10. 5ab*c xy? 2 2mn 2w2 +3w-5 S obiviaI :olqs Learning Task 3: Solve. 1. What is the area of the rectangle whose length is (x + 5) and width (x 5)? 2. What is the area of the square whose sides measure (3x + 4)? 3. The area of the rectangle is 3x2 + 7x - 6, what is the length if the width is (x +3) 4. What is the average speed of the car that covers a distance of (2y3-7y2 + 5y - 1) km in (2y-1) hour? olum 5. Multiply (m2 + 2m-2) by the sum of (m + 3 iand (2m - 3)
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