# Simplify: i) 2^{2/3}. 2^{1/5 }ii) (1/3^{3})^{7 }iii) 11^{1/2}/11^{1/4 }iv) 7^{1/2}. 8^{1/2}

**Solution:**

i) 2^{2/3}.2^{1/5}

Using exponent rules: a^{p} × a^{q} = a^{p + q} (For a > 0, where p and q are rational numbers)

= 2^{2/3 + 1/5}

= 2^{(10+3) /15}

= 2^{13/15}

ii) (1/3^{3})^{7}

Using exponent rules: (a^{p})^{q} = a^{pq} and 1/a^{-n} = a^{n }

(1/3^{3})^{7} = 1^{7}/ (3^{3})^{7}

= 1/3^{21}

= 3^{-21}

iii) 11^{1/2}/11^{1/4}

Using exponent rules: a^{p}/a^{q }= a^{p - q }

11^{1/2}/11^{1/4} = 11^{1/2 - 1/4}

= 11^{1/4}

iv) 7^{1/2}. 8^{1/2}

Using exponent rules: a^{p}.b^{p}^{ }= (a.b)^{p}

7^{1/2}. 8^{1/2} = (7 × 8)^{1/2 }

= 56^{1/2}

**☛ Check: **CBSE NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

**Video Solution:**

## Simplify:

i) 2²/³. 2¹/⁵^{ }ii) (1/3³)⁷^{ }iii) 11¹/² / 11¹/⁴^{ }iv) 7¹/². 8¹/²

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.6 Question 3:

**Summary:**

The simplified values of 2^{2/3}. 2^{1/5}, (1/3^{3})^{7}, 11^{1/2}/11^{1/4,} and 7^{1/2}. 8^{1/2} are 2^{13/15}, 3^{-21}, 11^{1/4} and 56^{1/2} respectively.

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