SIMPLIFYING EXPRESSIONS WITH RATIONAL EXPONENTS WORKSHEET

Simplify each of the following expressions : 

Question 1 :

y2/3 ⋅ y7/3

Question 2 :

a3/5 ⋅ a7/5

Question 3 :

(x4y)1/2

Question 4 :

(a1/2b1/3)2

Question 5 :

(2a1/2)(3a)

Question 6 : 

√(x4y2)

Question 7 : 

4√(x4y12)

Question 8 : 

(x1/3)⋅ 4√y4

Question 9 : 

[(x2y1/2)4⋅ [3√y3]

Question 10 : 

(xy1/2)2 / 5√x5

Answers

1. Answer :

=  y2/3 ⋅ y7/3

=  y2/3 + 7/3

=  y(2 + 7)/3

=  y9/3

=  y3

2. Answer :

=  a3/5 ⋅ a7/5

=  a(3 + 7)/5

=  a10/5

=  a2

3. Answer :

=  (x4y)1/2

=  (x4)1/2y1/2

=  x2y1/2

4. Answer :

=  (a1/2b1/3)2

=  (a1/2)2(b1/3)2

=  a1b2/3

5. Answer :

=  (2a1/2)(3a)

=  6a1/2 + 1

=  6a1/2 + 2/2

=  6a(1 + 2)/2

=  6a3/2

6. Answer :

=  √(x4y2)

=  (x4y2)1/2

=  (x4)1/2 ⋅ (y2)1/2

=  (x⋅ 1/2⋅ (y⋅ 1/2)

=  (x2⋅ (y1)

=  x2y

7. Answer :

=  4√(x4y12)

=  (x4y12)1/4

=  (x4)1/4 ⋅ (y12)1/4

=  (x⋅ 1/4⋅ (y12 ⋅ 1/4)

=  (x1⋅ (y3)

=  xy3

8. Answer :

=  (x1/3)⋅ 4√y4

=  (x1/3)⋅ (y4)1/4

=  x1/3 ⋅ ⋅ y⋅ 1/4

=  x⋅ y1

=  x2y

9. Answer :

=  [(x2y1/2)4⋅ [3√y3]

=  (x2y1/2)⋅ y

=   (x2)⋅ (y1/2)⋅ y

=   (x⋅ 4⋅ (y1/2 ⋅ 4⋅ y

=   x8 ⋅ y2 ⋅ y

=   x8 ⋅ y2 + 1

=   x8y3

10. Answer :

=  (xy1/2)2 / 5√x5

=  (x)2 ⋅ (y1/2)2 / x

=  x2 ⋅ y1/2 ⋅ 2 / x

=  x2 ⋅ y / x

=  x2 - 1 ⋅ y

=  xy

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