MULTIPLYING RATIONAL EXPONENTS WORKSHEET

Problem 1 :

Evaluate :

(27p⁶)^1/3

Problem 2 :

Evaluate :

(216x⁹)^1/3

Problem 3 : 

Evaluate : 

(42^1/3 / 6^1/3)^1/2

Problem 4 : 

Evaluate : 

(³√x² ⋅ ⁶√x⁴)^-3

Problem 5 : 

Evaluate : 

(³√x⁴ ⋅ √x⁵) / √(25x¹⁶)

Problem 6 :

Evaluate :

(5^1/3x^1/4)³

Problem 7 :

Evaluate :

√(8x³)√(18x)

Detailed Answer Key

Problem 1 :

Evaluate :

(27p⁶)^1/3

Solution :

=  (27p⁶)^1/3

=  (3³p⁶)^1/3

=  (3³)^1/3(p⁶)^1/3

=  3p²

Problem 2 :

Evaluate :

(216x⁹)^1/3

Solution :

=  (216x⁹)^1/3

=  (6³x⁹)^1/3

=  (6³)^1/3(x⁹)^1/3

=  6x³

Problem 3 : 

Evaluate : 

(42^1/3 / 6^1/3)^1/2

Solution :

=  (42^1/3 / 6^1/3)^1/2

=  [(42/6)^(1/3)]^1/2

  =  (7^(1/3))^1/2

=  7^1/6

Problem 4 : 

Evaluate : 

(³√x² ⋅ ⁶√x⁴)^-3

Solution : 

=  (³√x² ⋅ ⁶√x⁴)^-3

=  [(x²)^1/3 ⋅ (x⁴)^1/6]^-3

=  [x^2/3 ⋅ x^2/3]^-3

=  (x^4/3)^-3

=  x^-4

=  1/x⁴

Problem 5 : 

Evaluate : 

(³√x⁴ ⋅ √x⁵) / √(25x¹⁶)

Solution : 

=  (³√x⁴ ⋅ √x⁵) / √(25x¹⁶)

=  [(x⁴)^1/3 ⋅ (x⁵)^1/2] / (25x¹⁶)^1/2

=  (x^4/3 ⋅ x^5/2) / (5x⁸)

=  (x^{4/3 + 5/2 - 8}) / 5

=  (x^{8/6 + 15/6 - 48/6}) / 5

=  (x^-25/6) / 5

=  1 / (5x^25/6)

Problem 6 :

Evaluate :

(5^1/3x^1/4)³

Solution :

  =  (5^1/3x^1/4)³

= 5x^3/4

Problem 7 :

Evaluate :

√(8x³)√(18x)

Solution :

=  √(8x³ ⋅ 18x)

=  √(144x⁴)

=  (144x⁴)^1/2

=  12x²

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