#### Solved Examples and Worksheet for Expressions with Rational Exponents

Q1Evaluate:
34313

A. 11029
B. 1
C. 7
D. 3433

Step: 1
34313 = (73)13
Step: 2
= (7)3 13
[Use the formula (am)n = amn.]
Step: 3
= 7
Correct Answer is :   7
Q2Evaluate:
72913

A. 12187
B. 1
C. 9
D. 243

Step: 1
72913 = (93)13
Step: 2
= (9)3 13
[Use the formula (am)n = amn.]
Step: 3
= 9
Correct Answer is :   9
Q3Evaluate:
(- 216)23

A. - 144
B. 136
C. 36
D. - 36

Step: 1
(- 216)23 = (- 2163)2
[Use the formula amn = (an)m.]
Step: 2
= ((- 6)3 13)2 = (- 6)2 = 36
Correct Answer is :   36
Q4Evaluate:
1211.5

A. 3632
B. 121
C. 1331
D. 11

Step: 1
1211.5 = 12132
Step: 2
= (121)3
[Use the formula amn = (an)m.]
Step: 3
= (11)3
Step: 4
= 1331
Correct Answer is :   1331
Q5Simplify:
(625x- 16y20)- 14

A. x45y5
B. 625x4y5
C. 625x4y- 5
D. 15x4y5

Step: 1
(625x- 16y20)- 14 = 625- 14.x- 16(- 14). y20(- 14)
[Use: (albmcn)p = alp b mp cnp.]
Step: 2
= 162514 . x4 . y - 5
[Use: a - n = 1an.]
Step: 3
= 16254. x4 .1y5
[Use: a1n = an.]
Step: 4
= x45y5
Correct Answer is :   x45y5
Q6Evaluate:
(25)1.5

A. 121.5
B. 25
C. 5
D. 125

Step: 1
(25)1. 5 = 2532 = (25)3
[Use the formula amn = (an)m.]
Step: 2
= 53
Step: 3
= 125
Correct Answer is :   125
Q7Evaluate:
(- 16384)17

A. - 163847
B. 4
C. - 4
D. 163847

Step: 1
(- 16384)17 = (-47)17
Step: 2
= (-4)717
[Use the formula (am)n = amn.]
Step: 3
= - 4
Correct Answer is :   - 4
Q8Evaluate:
(64 84)- 56

A. 8- 536
B. 185
C. 140
D. 85

Step: 1
(64 84)- 56 = (8284)- 56
Step: 2
= (82 + 4)- 56
[Use am.an = am + n.]
Step: 3
= 86(- 56)
[Use (am)n = amn.]
Step: 4
= 8 - 5 = 185
[Use a - n = 1an .]
Step: 5
= 185
Correct Answer is :   185
Q9Evaluate:
7(- 512)- 13

A. 78
B. 35843
C. 56
D. - 78

Step: 1
7(- 512)- 13 = 7(- 512)13
[Use 1an = a-n.]
Step: 2
= 7- 5123
[Use a1n = an.]
Step: 3
= 7(-8)
Step: 4
= - 78
Correct Answer is :   - 78
Q10Evaluate:
27- 23

A. 19
B. 9
C. 3793
D. - 18

Step: 1
27- 23 = (33)- 23
Step: 2
33(- 23)
[Using (am)n = amn.]
Step: 3
= 3 - 2
[Use a - n = 1an.]
Step: 4
= 132
Step: 5
= 19
Correct Answer is :   19
Q11Simplify:
(9y23) - 1

A. - 9y3y
B. y39
C. 9y32
D. y39y

Step: 1
(9y23)-1 = 9 - 1 . y23(- 1)
[Use (ambn)p = ampbnp.]
Step: 2
= 9 - 1 . y- 23
Step: 3
= 19. 1y23
[Use a - n = 1an .]
Step: 4
= 19y23
Step: 5
= y39y
Correct Answer is :   y39y