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ASSIGNMENT PAGE

Study Guide and Intervention

Multiplying Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

6-18-1

©Glencoe/McGraw-Hill455Glencoe Algebra 1

Lesson 8-1

Multiply MonomialsA monomialis a number, a variable, or a product of a number and one or more variables. An expression of the form x nis called a powerand represents the product you obtain when xis used as a factor ntimes. To multiply two powers that have the same base, add the exponents. Product of PowersFor any number aand all integers mand n, am?an5am1 n.

Simplify (3x6)(5x?).

(3x

6)(5x2) 5(3)(5)(x6?x2)Associative Property

5(3 ?5)(x

6 1 2)Product of Powers

515x

8Simplify.

The product is 15x

8.Simplify (?4a

3b)(3a?b5).

(24a

3b)(3a2b5)5(24)(3)(a3?a2)(b?b5)

5 212(a

3 1 2)(b1 1 5)

5 212a

5b6

The product is 212a5b6.

Example1Example1Example2Example2

ExercisesExercises

Simplify.

?.y(y

5)?.n2?n73.(27x2)(x4)

4.x(x

2)(x4)5.m?m56.(2x3)(2x4)

7.(2a

2)(8a)8.(rs)(rs3)(s2)9.(x2y)(4xy3)

?0.(2a

3b)(6b3)??.(24x3)(25x7)??.(23j2k4)(2jk6)

?3.(5a }3

©Glencoe/McGraw-Hill456Glencoe Algebra 1

Powers of MonomialsAn expression of the form (xm)nis called a power of a power and represents the product you obtain when x mis used as a factor ntimes. To find the power of a power, multiply exponents. Power of a PowerFor any number aand all integers mand n, (am)n5amn. Power of a ProductFor any number aand all integers mand n, (ab)m5ambm.

Simplify (??ab?)3(a?)4.

(22ab

2)3(a2)45(22ab2)3(a8)Power of a Power

5(22)

3(a3)(b2)3(a8)Power of a Product

5(22)

3(a3)(a8)(b2)3Commutative Property

5(22)

3(a11)(b2)3Product of Powers

5 28a

11b6Power of a Power

The product is 28a

11b6.

Simplify.

?.(y

5)2?.(n7)43.(x2)5(x3)

4.23(ab

4)35.(23ab4)36.(4x2b)3

7.(4a2)2(b3)8.(4x)2(b3)9.(x2y4)5

1}5Study Guide and Intervention

(continued)

Multiplying Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

8-18-1

ExampleExample

ExercisesExercises

Skills Practice

Multiplying Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

8-18-1

©Glencoe/McGraw-Hill457Glencoe Algebra 1

Lesson 8-1

Determine whether each expression is a monomial. Write yesor no. Explain. ?.11 ?.a2b 3. 4.y 5.j 3k

6.2a13b

Simplify.

7.a

2(a3)(a6)8.x(x2)(x7)

9.(y

2z)(yz2)?0.(,2k2)(,3k)

??.(e

2f4)(e2f2)??.(cd2)(c3d2)

?3.(2x

2)(3x5)?4.(5a7)(4a2)

?5.(4xy

3)(3x3y5)?6.(7a5b2)(a2b3)

?7.(25m

3)(3m8)?8.(22c4d)(24cd)

?9.(10

2)3?0.(p3)12

??.(26p)2??.(23y)3 ?3.(3pq2)2?4.(2b3c4)2

GEOMETRY

Express the area of each figure as a monomial.

?5. ?6. ?7. 4p

9p3cdcd

x2 x5 p2}q2

©Glencoe/McGraw-Hill458Glencoe Algebra 1

Determine whether each expression is a monomial. Write yesor no. Explain.

Simplify.

3.(25x

2y)(3x4)4.(2ab2c2)(4a3b2c2)

5.(3cd

4)(22c2)6.(4g3h)(22g5)

7.(215xy

4)?2xy3?8.(2xy)3(xz)

9.(218m

2n)2?2mn2??0.(0.2a2b3)2

??.?p?

2??.?cd3?

2 ?3.(0.4k3)3?4.[(42)2]2

GEOMETRY

Express the area of each figure as a monomial.

?5. ?6. ?7. GEOMETRYExpress the volume of each solid as a monomial. ?8. ?9. ?0. COUNTINGA panel of four light switches can be set in 24ways. A panel of five light switches can set in twice this many ways. In how many ways can five light switches be set? HOBBIESTawa wants to increase her rock collection by a power of three this year and then increase it again by a power of two next year.If she has 2 rocks now, how many rocks will she have after the second year? 7g2 3g m3nmn 3 n

3h23h2

3h2 6ac3 4a2c 5x3 6a2b4 3ab2

1}42}31

}61 }3b 3c2 }221a2 }7bPractice

Multiplying Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

8-18-1

Study Guide and Intervention

Dividing Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

6-28-2

©Glencoe/McGraw-Hill461Glencoe Algebra 1

Lesson 8-2

Quotients of MonomialsTo divide two powers with the same base, subtract the exponents. Quotient of PowersFor all integers mand nand any nonzero number a, 5am?n.

Power of a QuotientFor any integer

mand any real numbers aand b, bÞ0, ? ? m5.am}bma}ba m}an

Simplify . Assume

neither anor bis equal to zero. 5 ? ?? ?Group powers with the same base. 5(a

4 ?1)(b7 ?2)Quotient of Powers

5a

3b5Simplify.

The quotient is a

3b5.b 7 }b2a4}aa

4b7}ab2a

4b7 }ab2Simplify 1 2 3.

Assume that bis not equal to zero.

35Power of a Quotient

5Power of a Product

5Power of a Power

5Quotient of Powers

The quotient is .

8a9b9 }278a9b9 }278a9b15 }27b62

3(a3)3(b5)3

}}(3)3(b2)3(2a3b5)3 }(3b2)32a3b5}3b22a3b5 }3b2Example1Example1Example2Example2

ExercisesExercises

Simplify. Assume that no denominator is equal to zero.

1. 2. 3.

4. 5. 6.

7. 8.

39.? ?3

10.? ?411.? ?412.r7s7t2}s3r3t23r6s3}2r5s2v5w3}v4w34p4q4

}3p2q22a2b}axy

6}y4x?2y7

}14y5x5y3}x5y2a2}ap 5n4 }p2nm

6}m455}52

©Glencoe/McGraw-Hill462Glencoe Algebra 1

Negative ExponentsAny nonzero number raised to the zero power is 1; for example, (?0.5)

051. Any nonzero number raised to a negative power is equal to the reciprocal of the

number raised to the opposite power; for example, 6 ?35. These definitions can be used to simplify expressions that have negative exponents.

Zero ExponentFor any nonzero number a, a051.

Negative Exponent PropertyFor any nonzero number

aand any integer n, a?n5and 5an. The simplified form of an expression containing negative exponents must contain only positive exponents. Simplify . Assume that the denominator is not equal to zero. 5 ? ?? ?? ?? ?Group powers with the same base. 5(a ?3 ?2)(b6 ?6)(c5)Quotient of Powers and Negative Exponent Properties 5a ?5b0c5Simplify. 5 ? ?(1)c

5Negative Exponent and Zero Exponent Properties

5Simplify.

The solution is .

Simplify. Assume that no denominator is equal to zero.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11.

012.(?2mn2)?3}}4m?6n44m2n2}8m?1,s

?3t?5}(s2t3)?1(3st)2u?4 }}s?1t2u7(6a?1b)2}}(b2)4x

4y0}x?2(a2b3)2

}(ab)?2(?x?1y)0}}4w?1y2b ?4}b?5p ?8 }p3m}m?422}2?3c 5 }4a5c 5 }4a51 }a51}41 }41 }41 }}16a2b6c?51 }a?n1}an

1}63Study Guide and Intervention

(continued)

Dividing Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

8-28-2

ExampleExample

ExercisesExercises

Skills Practice

Dividing Monomials

NAME ______________________________________________ DATE ____________ PERIOD _____

8-28-2

©Glencoe/McGraw-Hill463Glencoe Algebra 1

Lesson 8-2

Simplify. Assume that no denominator is equal to zero. 1.2. 3.4. 5.6. 7.8. 9.10.

11.12.

13.

214.4?4

15.8?216.? ??2

17.? ??118.

19.k

0(k4)(k?6)20.k?1(,?6)(m3)

21.22.? ?

0

23.24.

25.26.48x6y7z5

}}?6xy5z6?15w0u?1}}5u315x6y?9quotesdbs_dbs8.pdfusesText_14