# JAC Class 9 Maths Solutions Chapter 1 Number Systems Ex 1.6

Jharkhand Board JAC Class 9 Maths Solutions Chapter 1 Number Systems Ex 1.6 Textbook Exercise Questions and Answers.

## JAC Board Class 9th Maths Solutions Chapter 1 Number Systems Exercise 1.6

Question 1.
Find:
(i) $$64^{\frac{1}{2}}$$
(ii) $$32^{\frac{1}{5}}$$
(iii) $$125^{\frac{1}{3}}$$
(i) $$64^{\frac{1}{2}}=\left(2^6\right)^{\frac{1}{2}}=2^{6 \times \frac{1}{2}}=2^3=8$$
(ii) $$32^{\frac{1}{5}}=\left(2^5\right)^{\frac{1}{5}}=2^{5 \times \frac{1}{5}}=2$$
(iii) $$125^{\frac{1}{3}}=\left(5^3\right)^{\frac{1}{3}}=5^{3 \times \frac{1}{3}}=5$$

Question 2.
Find:
(i) $$9^{\frac{3}{2}}$$
(ii) $$32^{\frac{2}{5}}$$
(iii) $$16^{\frac{3}{4}}$$
(iv) $$125^{\frac{-1}{3}}$$
(i) $$9^{\frac{3}{2}}=\left(3^2\right)^{\frac{3}{2}}=3^3=27$$
(ii) $$32^{\frac{2}{5}}=\left(2^5\right)^{\frac{2}{5}}=2^2=4$$
(iii) $$16^{\frac{3}{4}}=\left(2^4\right)^{\frac{3}{4}}=2^3=8$$
(iv) $$125^{\frac{-1}{3}}=\frac{1}{(125)^{\frac{1}{3}}}=\frac{1}{\left(5^3\right)^{\frac{1}{3}}}=\frac{1}{5}$$
(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) $$7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}$$