**Evaluate integers raised to fractional exponents worksheet :**

Here we are going to see some practice questions on evaluating integers raised to rational exponents.

**Step 1 :**

Try to split the number which is in base as much as possible.

**Step 2 :**

Whenever we have power raised to another power, then we can multiply both the powers. If it is possible we can simplify.

(1) Simplify 9^(1/2)

(2) Simplify 343^(-4/3)

(3) Simplify 36^(3/2)

(4) Simplify (81 m⁶)^(1/2)

(5) Simplify (64 n^12)^(1/6)

(6) Simplify (x^6)^(1/2)

(7) Simplify (9n^4)^(1/2)

(8) Simplify (27)^(1/6)

(9) Simplify (100)^(6/4)

(10) Simplify (64a^6)^(1/6)

**Question 1 :**

Simplify 9^(1/2)

**Solution :**

**We can write 9 as the multiple of 3,**

**9 = 3 x 3 = 3**²

9^(1/2) = (3²)^(1/2)

= 3 ^(2 x 1/2)

= 3 ^1

= 3

Hence 3 is the answer.

**Question 2 :**

Simplify 343^(-4/3)

**Solution :**

**We can write 343 as the multiple of 7,**

**343 = 7**** x 7**** x 7**** = 7**³

343^(-4/3) = (**7**³)^(-4/3)

= **7^3 **x (-4/3)

= 7^-4

= 1/7^4

= 1/2401

Hence 1/2401 is the answer.

**Question 3 :**

Simplify 36^(3/2)

**Solution :**

**We can express 36 as the multiple of 6,**

**36 = 6**** x 6**** = 6**²

36^(3/2) = (6²)^(3/2)

= 6**^2 **x (3/2)

= 6^3

= 6 x 6 x 6

= 216

Hence 216 is the answer.

**Question 4 :**

Simplify (81 m⁶)^(1/2)

**Solution :**

**We can express 81 as the multiple of 9,**

**81 = 9**** x 9**** = 9**²

(81 m⁶)^(1/2) = (**9**²m⁶)^(1/2)

By distributing the power, we get

= (9²)^(1/2) (m⁶)^(1/2)

= 9 m^(6 x 1/2)

= 9 m^3

Hence 9 m^3 is the answer.

**Question 5 :**

Simplify (64 n^12)^(1/6)

**Solution :**

**We can express 64 as the multiple of 2,**

** 64 = 2**** x 2 ****x 2 ****x 2 ****x 2 ****x 2**** = 2**⁶

(64 n^12)^(1/6) = (**2**⁶ n^12)^(1/6)

By distributing the power, we get

= (**2**⁶)^(1/6) (n^12)^(1/6)

= 2 n^(12 x 1/6)

= 2 n^2

Hence 2 n^2 is the answer.

**Question 6 :**

Simplify (x^6)^(1/2)

**Solution :**

= x^(6(1/2))

= x^3

Hence x^3 is the answer.

**Question 7 :**

Simplify (9n^4)^(1/2)

**Solution :**

**We can express 9 as the multiple of 3,**

** 9 = 3**** x 3 = 3**²

(9n^4)^(1/2) = (3²n^4)^(1/2)

By distributing the power, we get

= (3²)^(1/2) (n^4)^(1/2)

= 3^(2 x 1/2) (n^(4 x 1/2)

= 3 n^2

Hence 3 n^2 is the answer.

**Question 8 :**

Simplify (27)^(1/6)

**Solution :**

**We can express 27 as the multiple of 3,**

** 27 = 3**** x 3 x 3 = 3**³

(27)^(1/6) = ( 3³)^(1/6)

By multiplying the power raised to another power, we get

= 3^3 x (1/6)

= 3^(1/2)

= √3

Hence √3 is the answer.

**Question 9 :**

Simplify (100)^(6/4)

**Solution :**

**We can express 100 as the multiple of 10,**

** 100 = 10**** x 10 = 10**²

(100)^(6/4) = (**10**²)^(6/4)

= 1**0^2 x **(6/4)

= 1**0^2 x **(3/2)

= 1**0^3**

= 10 x 10 x 10 = 1000

Hence the answer is 1000.

**Question 10 :**

Simplify (64a^6)^(1/6)

**Solution :**

**We can express 64 as the multiple 2,**

**64 = 2 x 2 x 2 x ****2 x 2 x 2**

** = 2^6**

**(64a^6)^(1/6) = (2^6a^6)^(1/6)**

** = (2a)^6^(1/6)**

** = 2a**

**Hence the answer is 2a.**

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