EVALUATE INTEGERS RAISED TO FRACTIONAL EXPONENTS WORKSHEET

Evaluate Integers Raised to Fractional Exponents Worksheet : 

Worksheet given in this section will be much useful for the students who would like to practice problems evaluating integers raised to fractional exponents.  

Evaluate Integers Raised to Fractional Exponents Worksheet - Problems

(1)  Evaluate : 9^1/2

(2)  Evaluate : 343^-4/3

(3)  Evaluate : 36^3/2

(4)  Evaluate : (81m⁶)^1/2

(5)  Evaluate : (64n¹²)^1/6

(6)  Evaluate : (x⁶)^1/2

(7)  Evaluate : (9n⁴)^1/2

(8)  Evaluate : 27^1/6

(9)  Evaluate : 100^6/4

(10)  Evaluate : (64a⁶)^1/6

Evaluate Integers Raised to Fractional Exponents Worksheet - Solutions

Problem 1 :

Evaluate : 9^1/2

Solution :

9^1/2  =  (3²)^1/2

9^1/2  =  3^2 ⋅ 1/2

9^1/2  =  3¹

9^1/2  =  3

Problem 2 :

Evaluate : 343^-4/3

Solution :

343^-4/3  =  (7³)^-4/3

343^-4/3  =  7^{3 ⋅ (-4/3)}

343^-4/3  =  7^-4

343^-4/3  =  7^-4

343^-4/3  =  1/7⁴

343^-4/3  =  1/7^-4

9^1/2  =  1/2401

Problem 3 :

Evaluate : 36^3/2

Solution :

36^3/2  =  (6²)^3/2

36^3/2  =  6^{2 ⋅ 3/2}

36^3/2  =  6³

36^3/2  =  216

Problem 4 :

Evaluate : (81m⁶)^1/2

Solution :

(81m⁶)^1/2  =  (3⁴m⁶)^1/2

(81m⁶)^1/2  =  (3⁴)^1/2(m⁶)^1/2

(81m⁶)^1/2  =  (3²)(m³)

(81m⁶)^1/2  =  9m³

Problem 5 :

Evaluate : (64n¹²)^1/6

Solution :

(64n¹²)^1/6  =  (2⁶n¹²)^1/6

(64n¹²)^1/6  =  (2⁶)^1/6(n¹²)^1/6

(64n¹²)^1/6  =  (2¹)(n²)

(64n¹²)^1/6  =  2n²

Problem 6 :

Evaluate : (x⁶)^1/2

Solution :

(x⁶)^1/2  =  x^6 ⋅ 1/2

(x⁶)^1/2  =  x³

Problem 7 :

Evaluate : (9n⁴)^1/2

Solution :

(9n⁴)^1/2  =  (3²n⁴)^1/2

(9n⁴)^1/2  =  (3²)^1/2(n⁴)^1/2

(9n⁴)^1/2  =  (3¹)(n²)

(9n⁴)^1/2  =  3n²

Problem 8 :

Evaluate : 27^1/6

Solution :

27^1/6  =  (3³)^1/6

27^1/6  =  3^3 ⋅ 1/6

27^1/6  =  3^1/2

27^1/6  =  √3

Problem 9 :

Evaluate : 100^6/4

Solution :

100^6/4  =  100^3/2

100^6/4  =  (10²)^3/2

100^6/4  =  10^{2 ⋅ 3/2}

100^6/4  =  10³

100^6/4  =  1000

Question 10 :

Evaluate : (64a⁶)^1/6 

Solution :

(64a⁶)^1/6  =  (2⁶a⁶)^1/6

(64a⁶)^1/6  =  (2⁶)^1/6(a⁶)^1/6

(64a⁶)^1/6  =  (2¹)(a¹)

(64a⁶)^1/6  =  2a

After having gone through the stuff given above, we hope that the students would have understood, how to evaluate integers raised to fractional exponents. 

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