The document Ex 1.6 NCERT Solutions - Number System Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Ques 1: Find: ****(i) 64 ^{1/2} **

âˆ´ (64)

= 8

Thus, 64

(ii) âˆµ 32 = 2 x 2 x 2 x 2 x 2 = 2

âˆ´ (3

= 2

Thus, (32)

(iii) âˆµ 125 = 5 x 5 x 5 = 53

âˆ´ (125)^{1/3} = (5^{3})^{1/3} = 5^{3x}^{1/3 }= 5^{1}

Thus, 125^{1/3} = 5

**Ques 2: Find:****(i) 9**^{3/2}** ****(ii) 32 ^{2/5} **

âˆ´ (9)

Thus, 9

(ii) âˆµ 32 = 2 x 2 x 2 x 2 x 2 = 2

âˆ´ (32)

Thus, 32^{2/5} = 4

(iii) âˆµ 16 = 2 x 2 x 2 x 2 = 2^{4}

âˆ´ (16)^{3/4} = (2^{4})^{3/4} = 2^{4x3/4} = 2^{3} = 8

Thus, 16^{3/4 }= 8

(iv) âˆµ 125 = 5 x 5 x 5 = 5^{3}

âˆ´ (125)^{â€“1/3} = (5^{3})^{â€“1/3} = 5^{3x(â€“1/3)} = 5â€“1 = 1/5

**Ques 3: Simplify:**

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

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

**Ans: **(i) âˆµ a^{m} . a^{n} = a^{m+n}

âˆ´ 2^{2/3} . 2^{1/5} = 2^{2/3 + 1/5}

= 2^{13/15 }

(ii) âˆµ^{ }

âˆ´

Thus,

(iii)

Thus,

(iv) âˆµ a^{m} . b^{m} = (ab)^{m}

âˆ´ 7^{1/2} . 8^{1/2} = (7 x 8)^{1/2} = (56)^{1/2}

Thus, 7^{1/2} . 8^{1/2 }= (56)^{1/2}

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