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Example 1 Example 2 Exercises Chapter 7 6 Glencoe Algebra 1 Study Guide and Intervention Multiplying Monomials NAME 

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Example 1Example 2

Exercises

Chapter 76Glencoe Algebra 1

Study Guide and Intervention

Multiplying Monomials

NAME ______________________________________________ DATE______________ PERIOD _____

7-17-1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Multiply MonomialsAmonomialis 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 mandn,am?an?am? n.

Simplify (3x6)(5x2).

(3x

6)(5x2)?(3)(5)(x6?x2)Group the coefficientsand the variables

?(3?5)(x

6? 2)Product of Powers

?15x

8Simplify.

The product is 15x

8.Simplify (?4a

3b)(3a2b5).

(?4a

3b)(3a2b5)?(?4)(3)(a3?a2)(b?b5)

? ?12(a

3? 2)(b1? 5)

? ?12a 5b6

The product is ?12a5b6.

Simplify.

1.y(y

5)2.n2?n73.(?7x2)(x4)

4.x(x

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

7.(2a

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

10.(2a

3b)(6b3)11.(?4x3)(?5x7)12.(?3j2k4)(2jk6)

13.(5a

?3

Exercises

Example

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 mandn, (am)n?amn. Power of a ProductFor any number aand all integers mandn, (ab)m?ambm.

Simplify (?2ab2)3(a2)4.

(?2ab

2)3(a2)4?(?2ab2)3(a8)Power of a Power

?(?2)

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

?(?2)

3(a3)(a8)(b2)3Group the coefficients and the variables

?(?2)

3(a11)(b2)3Product of Powers

? ?8a

11b6Power of a Power

The product is ?8a

11b6.

Simplify.

1.(y

5)22.(n7)43.(x2)5(x3)

4.?3(ab

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

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

1?5

Lesson 7-1

Study Guide and Intervention(continued)

Multiplying Monomials

NAME ______________________________________________ DATE______________ PERIOD _____

Chapter 7

7

Glencoe Algebra 1

7-1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Exercises

Study Guide and Intervention

Dividing Monomials

NAME ______________________________________________ DATE______________ PERIOD _____ 7-2

Chapter 713Glencoe Algebra 1

Lesson 7-2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Quotients of MonomialsTo divide two powers with the same base, subtract the exponents. Quotient of PowersFor all integers mandnand any nonzero number a,?am?n.

Power of a QuotientFor any integer

mand any real numbers aandb,b?0,? ? m?.am?bma?ba m?an

Simplify . Assume

neitheranorbis equal to zero. ? ?? ?Group powers with the same base. ?(a

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

?a

3b5Simplify.

The quotient is a

3b5.b 7 ?b2a4?aa

4b7?ab2a

4b7 ?ab2Simplify? ? 3.

Assume that bis not equal to zero.

3?Power of a Quotient

?Power of a Product ?Power of a Power ?Quotient of Powers

The quotient is .

8a9b9 ?278a9b9 ?278a9b15 ?27b62

3(a3)3(b5)3

??(3)3(b2)3(2a3b5)3 ?(3b2)32a3b5?3b22a3b5 ?3b2 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

Example 1Example 2

Exercises

Chapter 714Glencoe Algebra 1

Study Guide and Intervention (continued)

Dividing Monomials

NAME ______________________________________________ DATE______________ PERIOD _____ 7-2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Negative ExponentsAny nonzero number raised to the zero power is 1; for example, (?0.5)

0?1. Any nonzero number raised to a negative power is equal to the reciprocal of the

number raised to the opposite power; for example, 6 ?3?. These definitions can be used to simplify expressions that have negative exponents.

Zero ExponentFor any nonzero number a,a0?1.

Negative Exponent PropertyFor any nonzero number

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

5Negative Exponent and Zero Exponent Properties

?Simplify.

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?63

Example

Example

Exercises

Chapter 720Glencoe Algebra 1

Study Guide and Intervention

Polynomials

NAME ______________________________________________ DATE______________ PERIOD _____quotesdbs_dbs4.pdfusesText_8