SIMPLIFYING EXPRESSIONS WITH RATIONAL EXPONENTS WORKSHEET

Simplify each of the following expressions : 

Question 1 :

y^2/3 ⋅ y^7/3

Question 2 :

a^3/5 ⋅ a^7/5

Question 3 :

(x⁴y)^1/2

Question 4 :

(a^1/2b^1/3)²

Question 5 :

(2a^1/2)(3a)

Question 6 : 

√(x⁴y²)

Question 7 : 

⁴√(x⁴y¹²)

Question 8 : 

(x^1/3)⁶ ⋅ ⁴√y⁴

Question 9 : 

[(x²y^1/2)⁴] ⋅ [³√y³]

Question 10 : 

(xy^1/2)² / ⁵√x⁵

Answers

1. Answer :

=  y^2/3 ⋅ y^7/3

=  y^{2/3 + 7/3}

=  y^{(2 + 7)/3}

=  y^9/3

=  y³

2. Answer :

=  a^3/5 ⋅ a^7/5

=  a^{(3 + 7)/5}

=  a^10/5

=  a²

3. Answer :

=  (x⁴y)^1/2

=  (x⁴)^1/2y^1/2

=  x²y^1/2

4. Answer :

=  (a^1/2b^1/3)²

=  (a^1/2)²(b^1/3)²

=  a¹b^2/3

5. Answer :

=  (2a^1/2)(3a)

=  6a^{1/2 + 1}

=  6a^{1/2 + 2/2}

=  6a^{(1 + 2)/2}

=  6a^3/2

6. Answer :

=  √(x⁴y²)

=  (x⁴y²)^1/2

=  (x⁴)^1/2 ⋅ (y²)^1/2

=  (x^{4 ⋅ 1/2}) ⋅ (y^{2 ⋅ 1/2})

=  (x²) ⋅ (y¹)

=  x²y

7. Answer :

=  ⁴√(x⁴y¹²)

=  (x⁴y¹²)^1/4

=  (x⁴)^1/4 ⋅ (y¹²)^1/4

=  (x^{4 ⋅ 1/4}) ⋅ (y^{12 ⋅ 1/4})

=  (x¹) ⋅ (y³)

=  xy³

8. Answer :

=  (x^1/3)⁶ ⋅ ⁴√y⁴

=  (x^1/3)⁶ ⋅ (y⁴)^1/4

=  x^1/3 ⋅ 6 ⋅ y^{4 ⋅ 1/4}

=  x² ⋅ y¹

=  x²y

9. Answer :

=  [(x²y^1/2)⁴] ⋅ [³√y³]

=  (x²y^1/2)⁴ ⋅ y

=   (x²)⁴ ⋅ (y^1/2)⁴ ⋅ y

=   (x^{2 ⋅ 4}) ⋅ (y^{1/2 ⋅ 4}) ⋅ y

=   x⁸ ⋅ y² ⋅ y

=   x⁸ ⋅ y^{2 + 1}

=   x⁸y³

10. Answer :

=  (xy^1/2)² / ⁵√x⁵

=  (x)² ⋅ (y^1/2)² / x

=  x² ⋅ y^{1/2 ⋅ 2} / x

=  x² ⋅ y / x

=  x^{2 - 1} ⋅ y

=  xy

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