PROBLEMS INVOLVING RATIONAL EXPONENTS AND RADICALS

Simplify :

Problem 1 :

4^1/2

Solution :

=  4^1/2

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

=  (2²)^1/2

=  2 ^{2 x (1/2)}

=  2

So, the answer is 2.

Problem 2 :

225^1/2

Solution :

=  225^1/2

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

=  (15²)^1/2

=  15 ^{2 x (1/2)}

=  15

So, the answer is 15.

Problem 3 :

64^1/3

Solution :

=  64^1/3

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

=  (4³)^1/3

=  4 ^{3 x (1/3)}

=  4

So, the answer is 4.

Problem 4 :

1000^1/3

Solution :

=  1000^1/3

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

=  (10³)^1/3

=  10^{3 x (1/3)}

=  10

So, the answer is 10.

Problem 5 :

81^1/4

Solution :

=  81^1/4

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

=  (3⁴)^1/4

=  3^{4 x (1/4)}

=  3

So, the answer is 3.

Problem 6 :

32^1/5

Solution :

=  32^1/5

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

=  (2⁵)^1/5

=  2^{5 x (1/5)}

=  2

So, the answer is 2.

Problem 7 :

8^-1/3

Solution :

=  8^-1/3

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

=  (2³)^-1/3

=  2^{3 x (-1/3)}

=  2^-1

=  1/2

So, the answer is 1/2.

Problem 8 :

16^3/4

Solution :

=  16^3/4

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

=  (2⁴)^3/4

=  2^{4 x (3/4)}

=  2³

=  8

So, the answer is 8.

Problem 9 :

27^-2/3

Solution :

=  27^-2/3

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

=  (3³)^-2/3

=  3^{3 x (-2/3)}

=  3^-2

=  1/9

So, the answer is 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

So, the answer is 4/9.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.