# PROBLEMS INVOLVING RATIONAL EXPONENTS AND RADICALS

Simplify :

Problem 1 :

41/2

Solution :

=  41/2

By writing 4 in exponential form, we get 4  =  22

=  (22)1/2

=  2 2 x (1/2)

=  2

Problem 2 :

2251/2

Solution :

=  2251/2

By writing 225 in exponential form, we get 225  =  152

=  (152)1/2

=  15 2 x (1/2)

=  15

Problem 3 :

641/3

Solution :

=  641/3

By writing 64 in exponential form, we get 64  =  43

=  (43)1/3

=  4 3 x (1/3)

=  4

Problem 4 :

10001/3

Solution :

=  10001/3

By writing 1000 in exponential form, we get 1000  =  103

=  (103)1/3

=  103 x (1/3)

=  10

Problem 5 :

811/4

Solution :

=  811/4

By writing 81 in exponential form, we get 81  =  34

=  (34)1/4

=  34 x (1/4)

=  3

Problem 6 :

321/5

Solution :

=  321/5

By writing 32 in exponential form, we get 32  =  25

=  (25)1/5

=  25 x (1/5)

=  2

Problem 7 :

8-1/3

Solution :

=  8-1/3

By writing 8 in exponential form, we get 8  =  23

=  (23)-1/3

=  23 x (-1/3)

=  2-1

=  1/2

Problem 8 :

163/4

Solution :

=  163/4

By writing 64 in exponential form, we get 16  =  24

=  (24)3/4

=  24 x (3/4)

=  23

=  8

Problem 9 :

27-2/3

Solution :

=  27-2/3

By writing 27 in exponential form, we get 27  =  33

=  (33)-2/3

=  33 x (-2/3)

=  3-2

=  1/9

Problem 10 :

(2  1/4)-1/2

Solution :

=  (2  1/4)-1/2

By converting the mixed fraction into improper fraction, we get

=  (9/4)-1/2

=  ((3/2)2)-1/2

=  (3/2)-1

By flipping the base, we can change the negative exponent as positive.

=  2/3

Problem 11 :

(3  3/8)-2/3

Solution :

=  (3  3/8)-2/3

By converting the mixed fraction into improper fraction, we get

=  (27/8)-2/3

=  ((3/2)3)-2/3

=  (3/2)-2

By flipping the base, we can change the negative exponent as positive.

=  (2/3)2

=  4/9

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