#### Read L1.Exponent Properties - Multiplying and Dividing text version

`Name: ____________________________________Date: __________________Exponents and Their Properties - Multiplying and Dividing Monomials Algebra 1When we want to express a product of the same number like 3  3  3  3 we can use a shortcut notationexponent34baseThe exponent tells how many times the base is used as a factor in the product.Exercise #1: Write each of the following in the form of an expanded product.(a) x3 = (b) 45 = (c) ( 2x ) =3(d) ( x + 5 ) =2Exercise #2: Express each of the following with an equivalent expression involving exponents.(a) z  z  z  z  z = (d) x  x  y  y  y = (b) 6  6  6 = (e) ( x + y )( x + y )( x + y ) = (c) 2a  2a  2a  2a =Exercise #3: Consider the product shown below:x 4  x3(a) Write both parts of this product as extended products.x4 =x3 =(b) Write the product x 4  x3 as an expanded product and in terms of an equivalent expression involving an exponent.Exercise #4: Express each of the following products as a single variable raised to a power.(a) x 2  x 7 (b) x 6  x 2 (c) a 2  a 3  a 4 (d) y 2  y 6  y10Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540We also must be able to divide monomial expressions that have the same base. understanding how this process works is the following:The key toAny quantity divided by itself, except for zero, is equal to 1.x5 . x3(b) Rewrite the numerator of the quotient using (a).Exercise #5: Consider the quotient(a) Fill in the following: x5 = x 2  _______ .(c) Rewrite the quotient as the product of two fractions, one of them being equal to 1.(d) Simplify the quotient using the Multiplicative Identity Property of Real Numbers.Exercise #6: Fill in the blanks in the box below: EXPONENT PROPERTIESFor any real numbers a and b, 1. x  x = xa b_________xa 2. b = x _________ xExercise #7: Write each product or quotient in its simplest form.(a). (b) (c) (d) (e) (f) (g)a4  a4 = x2  x7 =(h)10 y 8 = 6 y23 3 =4 2(i)z3 = z2 b2 = b7 x2 y5 = x8 y 2y2  y6 =(j)23  2  2 4 = y5  y 2  y =(k)(x )32=(l)(x )23x4=Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540Name: ____________________________________Date: __________________Exponents and Their Properties - Multiplying and Dividing Monomials Algebra 1 Homework SkillExpress the product with exponents. 1. a  a  a b b = 2. 3. 17.x13 y 5 = x2 y9( 2 x )( 2 x )( 2 x ) = ( 2 x )( 2 x ) y  y =18.8 x5 y 3 = 4 x8 y10y4 = y419.Express the product in simplest form. b3  b = 4. 5. 6. 7. 8. 9. 10. 11.ReasoningSimplify. xc 20. = xd 21. 22. 23.3y 4  y9 =c&gt;dx 2  x3  x 4 = n4  n =y y =z ( 2z ) ( 2z ) =x 4a  x 2a =x3  x 6  x 4 = x5  x 2 y 2 a  y 3a = yaa a =4 2x3  x 7 =24.z4  z4 =Express the quotient in simplest form. x5 13. = x4 14.25.x3  x 4(x )22=a10 = a4 x5 = x8y6 = y1226.x4  y5 =15.Determine True or False for each. State the reason for your answer. x4 27. = 12 2 x 28.16.45 = 22 3 2Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540Name: ____________________________________Date: __________________Exponents and Their Properties ­ Multiplying and Dividing Monomials Additional Practice Problems SkillFind the product. 1. x5  x3 =2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.ReasoningFind each quotient. 43 20. = 421. x3 = xy2  y = y y y =4 2 6Simplify. 4 x3 32. = 4x33. t3  t 2 = taaaa = a6  a4 = t t =3 722.x5 = x2y4 = y2 t2 = t234.a · b3 = b223.35.( ab )ab 22=r5  r3 =x 4  x5 =y3  y8 = t t =24.36.x4 y 2 = x3 y 5 4x4 y2 = 2 xy 325.z5 = z3z9 = z537.w w  w w =2 226.38. 39.xa  xa =xa = xbx4 y7 z = x 2 yz 3 x4 y 2 = x4 y 2 xy 5 = x2 y 2 x2 y = x3 y 2p5  p 3  p = x 6  x3  x = h8  h 3 = x4  x2 =27.t9 = t353 = 528.40.29.y y=2p3 = p263 = 6341.xxx = m 23  m17 = b15  b5 =30.42.31.x12 = x1043.Algebra 1, Unit #6 ­ Quadratic Algebra ­ L1 The Arlington Algebra Project, LaGrangeville, NY 12540`

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