Gujarat Board Textbook Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.6
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
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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 })
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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 })