# MULTIPLYING RATIONAL EXPONENTS WORKSHEET

## About "Multiplying rational exponents worksheet"

Multiplying rational exponents worksheet :

Here we are going to see some practice questions on multiplying rational exponents.

## Multiplying rational exponents worksheet - Practice questions

 (1)  Evaluate the following (2)  Evaluate the following (3)  Evaluate the following

(4)  Evaluate the following

12^(1/8) x 12^(5/6)

(5)  Evaluate the following

[5^(1/3) x x^(1/4)]^3

(6)  Evaluate the following

√(8 x^3) x √(18 x)

(7)  Evaluate the following

(27p6)(1/3)

(8)  Evaluate the following

3x1/2 x2/3

(9)  Evaluate the following

(216 x9)1/3

(10)  Evaluate the following

4x2/x1/2

Question 1 :

Evaluate the following

Solution :

Here we have same power for the numerator and the denominator.

=  [(42/6)(1/3)]1/2

=  [7(1/3)]1/2

Since we have power raised to another power, we have to multiply these two powers.

=  7(1/6)

Question 2 :

Solution :

=  1/x^4

Question 3 :

Evaluate the following

Solution :

Instead of square root we can use 1/2 as power and cube root we can use 1/3 as power.

25 x^16 = (5 x^8)^2     [25 = 5 x 5]

=  [x^(4/3) x (x)^(5/2)]/[5 x^8)^2]^(1/2)

=  x^[(4/3) + (5/2)]/(5 x^8)

=  x^[(8 + 15)/6]/(5 x^8)

=  x^(23/6)/(5 x^8)

= (1/5) x^[(23/6) - 8]

= (1/5) x^(-25/6)

= 1/5 x^(25/6)

Hence 1/5 x^(25/6) is the answer.

Question 4 :

Evaluate the following

12^(1/8) x 12^(5/6)

Solution :

=  12^(1/8) x 12^(5/6)

= 12^[(1/8) + (5/6)]

To add the fractions 1/8 and 5/6 we have take L.C.M for the denominators.

L.C.M of (8, 6) = 24

To make 8 as 24 we have to multiply

= 12^[(3 + 20)/24]

= 12^(23/24)

Question 5 :

Evaluate the following

[5^(1/3) x x^(1/4)]^3

Solution :

=  [5^(1/3) x x(1/4)]3

Now we have to distribute power 3 for both 5^(1/3) and x^(1/4). So it becomes

= 5 x x(3/4)

= 5 x(3/4)

Hence 5 x^(3/4) is the answer.

Question 6 :

Evaluate the following

√(8 x3) x √(18 x)

Solution :

=  √(8 x3x √(18 x)

8 = √(2 x 2 x3) = 2x√(2 x)

18 x = √(3 x 3 x 2 x x) = 3(2 x)

√(8 x3x √(18 x)  =  [2x√(2 x)] [3(2 x)]

=  6 x (2 x)

=  12 x2

Question 7 :

Evaluate the following

(27p6)(1/3)

Solution :

=  (27p6)(1/3)

we can split this 27 as 3  3

=  (33p6)(1/3)

=  (33)(1/3)(p6)(1/3)

=  3p2

Question 8 :

Evaluate the following

3x1/2 x2/3

Solution :

=  3x1/2  x2/3

=   3x(1/2) + (2/3)

=   3x(3+4)/6

=   3x7/6

Question 9 :

Evaluate the following

(216 x9)1/3

Solution :

=  (216 x9)1/3

we can split this 216 as 6  6  6

=   (63 x9)1/3

Distributing the power for both the terms

=   (63 x9)1/3

=   (63)(1/3) (x9)1/3

=   6 x3

Question 10 :

Evaluate the following

4x2/x1/2

Solution :

=  4x2/x1/2

=  4x2x-1/2

=  4x(2-(1/2))

=  4x3/2

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