GSEB 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

GSEB Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.6

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

GSEB Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.6

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\(\frac { 1 }{ 2 }\)

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