ex 1.6 class 9

Shashee Kant Sharma September 15, 2020

Question 1:

Find:

(i)

64^{\frac{1}{2}}

(ii)

32^{\frac{1}{5}}

(iii)

125^{\frac{1}{3}}

Solution:

(i)

64^{\frac{1}{2}}

{(8 \times 8)}^{\frac{1}{2}}

{8^{2}}^{\times \frac{1}{2}}

8

(ii)

32^{\frac{1}{5}}

{(2 \times 2 \times 2 \times 2 \times 2)}^{\frac{1}{5}}

{2^{5}}^{\times \frac{1}{5}}

2

(iii)

125^{\frac{1}{3}}

{(5 \times 5 \times 5)}^{\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}}

Solution:

(i).

9^{\frac{3}{2}}

{3 \times 2}^{\frac{3}{2}}

{3^{2}}^{\times \frac{3}{2}}

3^{3} = 27

(ii)

32^{\frac{2}{5}}

(2 \times 2 \times 2 \times 2 \times 2)^{\frac{2}{5}}

{2^{5}}^{\times \frac{2}{5}}

4

(iii)

16^{\frac{3}{4}}

{(2 \times 2 \times 2 \times 2)}^{\frac{3}{4}}

{2^{4}}^{\times \frac{3}{4}}

2^{3} = 8

(iv)

125^{\frac{- 1}{3}}

{(5 \times 5 \times 5)}^{\frac{- 1}{3}}

{5^{3}}^{\times \frac{- 1}{3}}

5^{- 1} = \frac{1}{5}

Question 3:

Simplify:

(i)

2^{\frac{2}{3}} {.2}^{\frac{1}{5}}

(ii)

(3^{\frac{1}{3}})^{7}

(iii)

\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}

(iv)

7^{\frac{1}{2}} {.8}^{\frac{1}{2}}

Solution 3:

(i)

2^{\frac{2}{3}} {.2}^{\frac{1}{5}}

2^{\frac{2}{3} + \frac{1}{5}}

2^{\frac{10 + 3}{15}}

2^{\frac{13}{15}}

(ii)

(3^{\frac{1}{3}})^{7}

(3)^{\frac{7}{3}}

(iii)

\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}

11^{\frac{1}{2} - \frac{1}{4}}

11^{\frac{2 - 1}{4}}

11^{\frac{1}{4}}

(iv)

7^{\frac{1}{2}} {.8}^{\frac{1}{2}}

{(7 \times 8)}^{\frac{1}{2}}

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

Class-9 Linear equation in two variables Ex 4.1