Gujarat Board GSEB Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.6 Textbook Questions and Answers.
Gujarat Board Textbook Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.6
Question 1.
Find
(i) 64^{\frac{1}{2}}
(ii) 32^{\frac{1}{5}}
(iii) 125^{\frac{1}{3}}
Solution:
(i) 64^{\frac{1}{2}} = \left(8^{2}\right)^{\frac{1}{2}} = 8^{2 \times \frac{1}{2}} = 81 = 8
(ii) 32^{\frac{1}{5}} = \left(2^{5}\right)^{\frac{1}{5}} = 2^{5 \times \frac{1}{5}} = 21 = 2
(iii) 125^{\frac{1}{3}} = \left(5^{3}\right)^{\frac{1}{3}} = 5^{3 \times \frac{1}{3}} = 51 = 5
Question 2.
Find
(i) 9^{\frac{3}{2}}
(ii) 32^{\frac{2}{5}}
(iii) 16^{\frac{3}{4}}
(iv) 125^{-\frac{1}{3}}
Solution:
(i) 9^{\frac{3}{2}} = \left(3^{2}\right)^{\frac{3}{2}} = 3^{2 \times \frac{3}{2}} = 33 = 3 x 3 x 3 = 27
(ii) 32^{\frac{2}{5}} = \left(2^{5}\right)^{\frac{2}{5}} = 3^{5 \times \frac{2}{5}} = 22 = 2 x 2 = 4
(iii) 16^{\frac{3}{4}} = \left(2^{4}\right)^{\frac{3}{4}} = 2^{4 \times \frac{3}{4}} = 23 = 8
(iv) 125^{-\frac{1}{3}} = (53)\frac { 1 }{ 3 } = 5^{3 \times-\frac{3}{4}} = 5-1 = \frac { 1 }{ 5 }
Question 3.
Simplify:
(i) 2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}}
(ii) \left(\frac{1}{3^{3}}\right)^{7}
(iii) \frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}
(iv) 7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}
Solution:
(i) 2^{\frac{2}{3}} \cdot 2^{\frac{1}{5}} = 2^{\frac{2}{3}} + 2^{\frac{1}{5}} = 2\frac { 2×5+3×1 }{ 15 } = 2\frac { 10+3 }{ 15 } = 2\frac { 13 }{ 15 }
(ii) \left(\frac{1}{3^{3}}\right)^{7} = \frac{1}{\left(3^{3}\right)^{7}} = \frac{1}{3^{21}} = 3-21
(iii) \frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}} = 11\frac { 1 }{ 2 } – \frac { 1 }{ 4 } = 11\frac { 1 }{ 4 }
(iv) 7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}} = (7 x 8)\frac { 1 }{ 2 } [am x bm = (a x b)m]
= 56\frac { 1 }{ 2 }