7-1 Study Guide and Intervention - Weebly

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7-1 Study Guide and Intervention

Multiplication Properties of Exponents

Multiply Monomials A monomial is a number, a variable, or the product of a number and one or more variables with nonnegative integer exponents. An expression of the form is called a power and represents the product you obtain when x is used as a factor n times. To multiply two powers that have the same base, add the exponents.

Product of Powers

For any number a and all integers m and n, = +.

Example 1: Simplify (3)(5).

(36)(52) = (3)(5)(6 2)

Group the coefficients and the variables

= (3 5)(6 + 2) Product of Powers

= 158

Simplify.

The product is 158.

Example 2: Simplify (?4b)(3). (?43b)(325) = (?4)(3)(3 2)(b 5)

= ?12(3 + 2)(1 + 5) = ?1256 The product is ?1256.

Exercises Simplify each expression.

1. y(5) y6

2. 2 7 n9

3. (?72)( 4) ?7x6

4. x(2)(4) x7

5. m 5 m6

6. (?3)(? 4) x7

7. (22)(8a) 16a3

8. (r n)(r 3)(2) r2n6

9. (2y)(4x3) 4x3y4

10. 13(23b)(63) 4a3b4

11. (?43)(?57) 20x10

12. (?324)(2j6) ?6j3k10

13.

(52b3)( a3b2c7

15ab

4)

14. (?5xy)(42)(4) ?20x3y5

15. (103y2)(?2x5z) ?20x4y6z3

Chapter 5

5

Glencoe Algebra 1

NAME _____________________________________________ DATE ____________________________ PERIOD _____________

7-1 Study Guide and Intervention (continued)

Multiplication Properties of Exponents

Simplify Expressions An expression of the form () is called a power of a power and represents the product you obtain when is used as a factor n times. To find the power of a power, multiply exponents.

Power of a Power Power of a Product

For any number a and any integers m and p, () = . For any numbers a and b and any integer m, () = .

We can combine and use these properties to simplify expressions involving monomials.

Example: Simplify (-)()4. (-22)3 (2)4 = (-22)3(8)

= (-2)3(3) ( 2)3 (8) = (-2)3(3)( 8) ( 2)3 = (-2)3(11) ( 2)3 = ?8116 The product is ?8116.

Power of a Power Power of a Product Group the coefficients and the variables Power of a Product Power of a Power

Exercises

Simplify each expression. 1. (5)2

y10

2. (7)4 n28

3. (2)5(3) x13

4. ?3(4)3 ?3a3b12

7. (42)2(3) 16a4b3

5. (-34)3 ?27a3b12

8. (4)2(3) 16x2b3

6. (42)3 64x6b3

9. (24)5 x10y20

10. (232)( 3)2 2a3b8

11. (-4)3(-22)3 512x9y3

12. (-323)2(22)3 72j10k9

13.

(252

)3

(1

5

2

)

625a8b5f 2

14. (2)2(?32)(44) ?48x4y6

15. (2322)3(2)4 8x17y6z10

16. (?265)(?632)()3 12n12y10

17. (?334)(-33)4 ?243a15n8

18. ?3(2)4(45)2 ?768x14y2

Chapter 7

6

Glencoe Algebra 1

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