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) \(125^{\frac{1}{3}}\)
Answer:
(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) \(125^{\frac{-1}{3}}\)
Answer:
(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) \(125^{\frac{-1}{3}}=\frac{1}{(125)^{\frac{1}{3}}}=\frac{1}{\left(5^3\right)^{\frac{1}{3}}}=\frac{1}{5}\)
Question 3.
(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) \(7^{\frac{1}{2}} \cdot 8^{\frac{1}{2}}\)
Answer:
