# Fractional Exponent Worksheet

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```					                   Worksheet #8—Basic Arithmetic Fractional Exponent Problems
E. White
Fall 2004

Simplify each of the following. Leave no exponents in your ﬁnal answer.

(1) 9−2                               (2) 82/3                           (3) 322/5
−2
1                                      −3/5
(4) 27−1/3                            (5)                                (6) (−32)
2
3/2                           2
4                               2
(7) 161/2                             (8)                                (9)
81                               3
−2                                                                           −2/3
4                                            2/3                          1
(10)                                  (11) (−8)                          (12)
9                                                                        64

(13) 50                               (14) 16−3/4                        (15) 4−2
−1                                       −1
1                                  1
(16) 1−2                              (17) −                             (18)   −
8                                  8
−2                                   1/2                               −2/3
1                                  9                                8
(19)   −                              (20)                               (21)
8                                 16                               27

(22) 4−5/2                            (23) 1441/2                        (24) 271/3

(25) 8−2                              (26) 4−3/2                         (27) 253/2

(28) 641/6                            (29) 100−1/2                       (30) 641/3

(31) 161/4                            (32) 82/3                          (33) 4−1/2
−3/2
1
(34) 642/3                            (35)                               (36) 41/2 + 9−1/2
9
3                                                                        3/2
1                                            −1/3                        4
(37)                                  (38) (−8)                          (39)
2                                                                        9
−2                                        1/2
2                                       1
(40)                                  (41)                               (42) 27−1/3
3                                       4
−1
(43) (−9)                             (44) 643/2                         (45) 321/5

−3
(46) (−8)                             (47) 3−1 5−2                       (48) 641/3

(49) 125−2/3                          (50) 36−3/2                        (51) 32−2/5
0
2
(52) 64−1/2                           (53) 41/2 81/3                     (54)
5
(55) 82/6                    (56) 11−2                     (57) 81−3/2

3/2
(58)     41/3                (59) 729−1/3                  (60) 3−2 + 2−3
−3/2                          2/3                      −2/3
4                       8                             1
(61) 3                       (62)                          (63)
9                      125                           27
3/2
64                                                             3/2
(64)                         (65) 16−1/4                   (66)   108
9
−2/3                            1/2
(67) 53/4 51/4               (68) 4 (8)                    (69) (−1)
−2                  2/3       6                      2/3
4                      2                         216
(70)     −                   (71)                          (72)
9                      3                         729
−2/3
1
(73)                         (74) 4−5/2                    (75) 1252/3
64
−3                                   −3                           −2
2                                  2                            2
(76)                         (77)   −                      (78)   −
3                                  3                            3
−1
7
(79)                         (80) 49−1/2                   (81) 1000−2/3
11
1                                                           1                                    1                               8
Answers:     (1)                    (2) 4              (3) 4          (4)                 (5) 4          (6) −             (7) 4           (8)
81                                                          3                                    8                              729
4             81                                                                                        1                  1
(9)           (10)                    (11) 4               (12) 16                  (13) 1             (14)              (15)               (16) 1
9             16                                                                                        8                  16
3                    9               1
(17) −8            (18) −8             (19) 64                 (20)                 (21)                (22)               (23) 12          (24) 3
4                    4              32
1                      1                                                                   1
(25)               (26)                (27) 125                (28) 2                (29)                 (30) 4           (31) 2           (32) 4
64                     8                                                                  10
1                                                              7                     1                 1                 8                   9
(33)          (34) 16                 (35) 27              (36)                    (37)               (38) −             (39)               (40)
2                                                              3                     8                 2                27                   4
1                  1                    1                                                              1                  1
(41)          (42)                  (43) −                 (44) 512                (45) 2             (46) −              (47)              (48) 4
2                  3                    9                                                             512                75
1                       1                       1                   1                                                                     1
(49)               (50)                     (51)               (52)                  (53) 4             (54) 1           (55) 2           (56)
25                     216                      4                   8                                                                    121
1                                          1                  17                    81                  4                               512
(57)               (58) 2             (59)                 (60)                    (61)                (62)              (63) 9           (64)
729                                         9                  72                    8                  25                                27
1                                                                                                                         81              16
(65)           (66) 1000000000000                          (67) 5                  (68) 1             (69) i            (70)               (71)
2                                                                                                                         16              81
4                                      1                                           27                   27                     9          11
(72)          (73) 16                (74)                  (75) 25             (76)                   (77) −              (78)             (79)
9                                      32                                           8                    8                     4           7
1                   1
(80)          (81)
7                  100

```
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