Bihar Board Class 9 Maths Solutions Chapter 1 संख्या पद्धति Ex 1.6 Text Book Questions and Answers.

## BSEB Bihar Board Class 9 Maths Solutions Chapter 1 संख्या पद्धति Ex 1.6

प्रश्न 1.

ज्ञात कीजिए

(i) 64^{\(\frac{1}{2}\)}

(ii) 32^{\(\frac{1}{5}\)}

(iii) 125^{\(\frac{1}{3}\)}

हाल:

(i) (64)^{\(\frac{1}{2}\)} = (8 × 8)\(\frac{1}{2}\)

= (8²)\(\frac{1}{2}\) [∵ (x^{a})^{b} = x^{ab}]

= 8

(ii) 32^{\(\frac{1}{5}\)} = (2 × 2 × 2 × 2 × 2)\(\frac{1}{5}\)

= (2^{5})\(\frac{1}{5}\)

= 2^{5×\(\frac{1}{5}\) } [∵ (x^{a})^{b} = x^{ab}]

= 2

(iii) 125^{\(\frac{1}{3}\)} = (5 × 5 × 5)\(\frac{1}{3}\)

= (5^{3})\(\frac{1}{3}\)

= 5^{3×\(\frac{1}{3}\) } [∵ (x^{a})^{b} = x^{ab}]

= 5

प्रश्न 2.

ज्ञात कीजिए

(i) 9^{\(\frac{3}{2}\)}

(ii) 32^{\(\frac{2}{5}\)}

(iii) 16^{\(\frac{3}{4}\)}

(iv) 125^{\(\frac{-1}{3}\)}

हल:

(i) 9^{\(\frac{3}{2}\)} = (3 × 3)\(\frac{3}{2}\)

= (3^{2})\(\frac{3}{2}\)

= 3^{2×\(\frac{3}{2}\) } [∵ (x^{a})^{b} = x^{ab}]

= 3³

= 27

(ii) 32^{\(\frac{2}{5}\)} = (2 × 2 × 2 × 2 × 2)\(\frac{2}{5}\)

= (2^{5})\(\frac{2}{5}\)

= 2^{5×\(\frac{2}{5}\) } [∵ (x^{a})^{b} = x^{ab}]

= 2²

= 4

(iii) 16^{\(\frac{3}{4}\)} = (2 × 2 × 2 × 2)\(\frac{3}{4}\)

= (2^{4})\(\frac{3}{4}\)

= 2^{4×\(\frac{3}{4}\) } [∵ (x^{a})^{b} = x^{ab}]

= 2³

= 8

(iv) 125^{\(\frac{-1}{3}\)} = (5 × 5 × 5)-\(\frac{1}{3}\)

= (5^{3})-\(\frac{1}{3}\)

= 5^{3×-\(\frac{1}{3}\) } [∵ (x^{a})^{b} = x^{ab}]

= 5^{-1}

= \(\frac{1}{5}\) [∵ (x^{-a}) = \(\frac{1}{x^a}\)]

प्रश्न 3.

सरल कीजिए

(i) 2^{\(\frac{2}{3}\)}. 2^{\(\frac{1}{5}\)}

(ii) (\(\frac{1}{3³}\))^{7}

(iii) \(\frac{11^\frac{1}{2}}{11^\frac{1}{4}}\)

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

हल:

(i) 2^{\(\frac{2}{3}\)}. 2^{\(\frac{1}{5}\)} = 2^{(\(\frac{2}{3}\)+\(\frac{1}{5}\))} [∵ x^{a}x^{b} = x^{a+b}]

= 2^{\(\frac{10+3}{5}\)}

= 2^{13/15}

(ii) (\(\frac{1}{3³}\))^{7} = \(\frac{1}{3^{3×7}}\) [∵ (x^{a})^{b} = x^{ab}]

= \(\frac{1}{3^{21}}\)

= 3^{-21}

(iii) \(\frac{11^\frac{1}{2}}{11^\frac{1}{4}}\) = 11^{\(\frac{1}{2}\) – \(\frac{1}{4}\)} [∵ \(\frac{x^a}{x^b} = x^{a-b}\)]

= 11^{\(\frac{2-1}{4}\)}

= 11^{\(\frac{1}{4}\)}

(iv) 7^{1/2}.8^{1/2} = (7.8)^{\(\frac{1}{2}\)} [∵ x^{a}y^{a} = (xy)^{a}]

= (56)^{1/2}