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 })} [a^m x b^m = (a x b)^m]
= 56^{(frac { 1 }{ 2 })}