Answer Learning Task 1, 2, and 3 Laws of Exponents and Its ApplicationWEEKILesson5In the process of multiplication and division of polynomials you need toapply the laws of exponents. Remember that exponent tells how many times thebase will be multiplied by itself. Any number an, a is the base and n is theexponent.53 means 5-5 125XHx XXx, the variable x ismultiplied by it self 5 times, hence you can write it as x5. Here, the base is x andthe exponent is 5DLearning Task 1Simplify by writing in exponential formWrite in expanded form1. 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 Exponents1. Product Law of Exponent.Any numbers m and integers x and y, m* -m = m*+yThe base must be the same before you can add the exponents.Example: b-b (b-b)(b.b.b) = bSimilarly:b2.63 =62+3 =b%2 Quotient Law of ExponentsAny numbers m and integers x and y,m*=m* =1, if x = ym*1m*, if x > yif x < yammmExamples:a5a a a aaa5a.a= a a a = a3 similarly= a3a3b.a3a a aAny number raised to zero= a3-3 = a0 = 1=1 similarlya3is always equal to 1a a aa?a aa21similarifua+a2a?D.v. v.D18 Subtract. 43 cannot be divided by x. Hence 43 1s the re-43 mainder20x -4043The quotient is 6x2 + 9x + 20 R. 43 or 6x2 + 9x + 20 +21ELearning Task 2:A. SimplifyB. Perform the indicated operations. Simplify your answer1. (-m4)37. 16a b'c'-24a'he +44a'b'c4a bc1. 2ab( 4a2 + 3ab 7b2).arm210c2. -3xy(x³y3 - 3x2y + 7xy2)2.2d330c? +19ac-63a?8.3. (x+ 2)(x2 -3x + 2)6c-7a3. (3a?bc)34. (2x 1)(2x2 + 4x + 3)4. (2x3y2z)(3x?yz?)5. (12y2 -9y + 16)(8y3 -14y + 5) 9. (a6 + b6) (a2 +6.25a b'c3m2n5.6w +7w? -12w +1510.5ab*cxy?22mn2w2 +3w-5S obiviaI :olqsLearning 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?olum5. Multiply (m2 + 2m-2) by the sum of (m + 3 iand (2m - 3)

Since this is a multiple question type question, according to the Bartleby answering rule, only…

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 (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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©Common Core Performance Assessment County Fair At the county fair, animals are judged for the quality of their breeding and health. The animal pens are arranged in an array, with one animal in each pen. A barn can hold at most 10 rows of pens and at most 6 pens in each row, with room for people to walk around them. What different ways can the planners of the county fair arrange the pens for the horses and cows in the same barn? 4. MP.2 Reasoning How do the quantities given in the problem relate to each other? 22 cows 5. MP.1 Make Sense and Persevere What steps do you need to do first? Explain. When yo you find an for solving can be simi 6. MP.4 Model with Math What are all the factor pairs for the sum of the horses and cows? Represent the factors with a diagram to show how you found all the factor pairs. 7. MP.6 Be Precise What are all the different ways the planners can arrange the pens for the horses and cows in the barn?
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