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Study Guide and Intervention

Negative Exponents

NAME ______________________________________________ DATE ______________ PERIOD _____

4-74-7©Glencoe/McGraw-Hill195Glencoe Pre-Algebra

Extending the pattern below shows that 4

-1 1 4 ?or? 41
1 4 2 ?16 ?4 4 1 ?4 ?4 4 0 ?1 ?4 4 ?1 1 4

This suggests the following definition.

a ?n a1 n ?, for a?0 and any integer n.

Write each expression using a positive exponent.

a. 3 ?4 b.y ?2 3 ?4 31
4 ?y ?2 y1 2 We can evaluate algebraic expressions with negative exponents using the definition of negative exponents.

Write each expression using a positive exponent.

1.6 4? 61
4 ?2.(?7) ?8 (?1 7) 8 ?3.b ?6 b1 6 ?4.n ?1 n1 1 ?or? n1 Write each fraction as an expression using a negative exponent other than?1. 5. 212
?2 ?2 6.? 11 3 4 ?13 ?4 7.? 21
5 ?5 ?2 8.? 41
9 ?7 ?2

Evaluate each expression if m??4,n ?1, and p?6.

9.p ?2 31

6?10.m

?3 61
4 ?11.(np) -1 1 6 ?12.3 m 81
1

Evaluate b

?2 if b?3. b ?2 ?3 ?2

Replacebwith 3.

312
?Definition of negative exponent 1 9 ?Find 3 2

Example 1Example 1

Example 2Example 2ExercisesExercises

Lesson 4-7

©Glencoe/McGraw-Hill196Glencoe Pre-Algebra

Skills Practice

Negative Exponents

NAME ______________________________________________ DATE ______________ PERIOD _____

4-74-7

Write each expression using a positive exponent.

1.3 ?4 31
4 ?2.8 ?7 81
7 ?3.10 ?4 11 0 4

4.(?2)

?6 (?1 2) 6 ?5.(?40) ?3 (?41 0) 3 ?6.(?17) ?12 (?11 7) 12 7.n ?10 n1 10 ?8.b ?8 b1 8 ?9.q ?5 q1 5 10.m ?4 m1 4 ?11.v ?11 v1 11 ?12.p ?2 p1 2 Write each fraction as an expression using a negative exponent other than ?1. 13. 81
2 ?8 ?2 14.? 11 0 5 ?10 ?5 15.? 21
3 ?2 ?3 16.? 61
7 ?6 ?7 17.? 11 7 4 ?17 ?4 18.? 21
1 2 ?21 ?2 19.? 31
7 ?3 ?7 20.? 91
2 ?9 ?2 21.?
31
2 ?3 ?2 22.?
11 21
?11 ?2 23.?
21
5 ?5 ?2 24.?
31
6 ?6 ?2

Evaluate each expression if x?1,y?2, and z??3.

25.y
?z 826.z
?2 1 9 ?27.x ?8 1 28.y
?5 31
2 ?29.z ?3 21
7 ?30.y ?1 1 2 31.z
?4 81
1 ?32.5 z 11 25
?33.x ?99 1 34.1
z 135.4
z 61
4 ?36.y z 1 8

Practice

Negative Exponents

NAME ______________________________________________ DATE ______________ PERIOD _____

4-74-7

©Glencoe/McGraw-Hill197Glencoe Pre-Algebra

Write each expression using a positive exponent.

1.7 ?8 71
8 ?2.10 ?6 11 0 6 ?3.23 ?1 21
3 1

4.(?5)

?2 (?1 5) 2 ?5.(?18) ?10 (?11 8) 10 ?6.m ?99 m1 99

7.(?1)

?12 (?11 12 ?8.c ?6 c1 6 ?9.p ?5 p1 5 10.g ?17 g1 17 ?11.5z ?4 5 z1 4 12.3t ?1 3 1 t Write each fraction as an expression using a negative exponent. 13. 21
10 ?2 ?10 14.? 21
9 3 ?29 ?3 15.? 41
4 ?4 ?4 16.? 31
9 ?39 ?1 17.? 81
1 7 ?81 ?7 18.? m1 4 ?m ?4 19.? x1 3 ?x ?3 20.? a1 2 ?a ?2 21.?
41
9 ?7 ?2 22.?
1 8 ?2 ?3 23.?
11 44
?12 ?2 24.?
11 69
?13 ?2

Evaluate each expression if x?3,y??2, and z ?4.

25.x
?4 81
1 ?26.y ?2 1 4 ?27.y ?5 31
2 28.z
?4 21
56
?29.5 y 21
5 ?30.10 y 11 00 31.3z
?1 3 4 ?32.z y 11 6 ?33.(xz) ?2 11 44

34.HAIRHair grows at a rate of ?

61
4 ?inch per day. Write this number using negative exponents.quotesdbs_dbs7.pdfusesText_13
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