# 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

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$$\frac { 1 }{ 2 }$$