9th Maths 1.6

NCERT Class 9th solution of Exercise 1.1

NCERT Class 9th solution of Exercise 1.2

NCERT Class 9th solution of Exercise 1.3

NCERT Class 9th solution of Exercise 1.4

NCERT Class 9th solution of Exercise 1.5

NCERT Class 9th Maths Projects

Exercise 1.6

Q1. Find : i) `64^frac{1}{2}` ii) `32^frac{1}{5}` iii) `125^frac{1}{3}`

Sol. : 

i) `64^frac{1}{2}` 

`= (8^2)^(frac{1}{2})` 

`= 8^(frac{1}{2}×2)` 

`= 8^1` 

`= 8`

Answer

 `= 8`

ii) `32^frac{1}{5}` 

`= (2^5)^frac{1}{5}` 

`= 2^(5×frac{1}{5})` 

`= 2`.

Answer

 `= 2`

iii) `125^frac{1}{3}`

`= (5^3)^frac{1}{3}` 

`= 5^(3×frac{1}{3})` 

`= 5`

Answer

 `= 5`

 

Q2. Find : i) `9^frac{3}{2}` ii) `32^frac{2}{5}`  iii) `16^frac{3}{4}`  iv) `125^frac{-1}{   3}`

Sol. :

i) `9^frac{3}{2}` 

`= (3^2)^frac{3}{2}` 

`= 3^(2×frac{3}{2})` 

`= 3^3` 

`= 27`.

Answer

 `= 27`

ii)  `32^frac{2}{5}` 

`= (2^5)^frac{2}{5}` 

`= 2^(5×frac{2}{5})` 

`= 2^2` 

`= 4`

Answer

 `= 4`

iii)  `16^frac{3}{4}` 

`= (2^4)^frac{3}{4}` 

`= 2^(4×frac{3}{4})` 

`= 2^3` 

`= 8`

Answer 

`= 8`

iv)  `125^frac{-1}{  3}` 

`= (5^3)^frac{-1}{  3}` 

`= 5^(3×frac{-1}{  3})` 

`= 5^(-1)` 

`= frac{1}{5}`

Answer

`= frac{1}{5}`

Q3. Simplify : i) `2^frac{2}{3}.2^frac{1}{5}`  ii) `(frac{1}{3^3})^7` iii)  `frac{11^frac{1}{2}}{11^frac{1}{4}}`  iv) `7^frac{1}{2}.8^frac{1}{2}`

Sol. :

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}`

Answer :

`= 2^frac{13}{15}`

ii) `(frac{1}{3^3})^7` 

`= frac{1}{3^3×7}` 

`= frac{1}{3^21}` 

`= 3^{-21}`

Answer :

 `= 3^{-21}`

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}`

Answer :

`= 11^frac{1}{4}`

iv) `7^frac{1}{2}.8^frac{1}{2}` 

`=  7^frac{1}{2}×8^frac{1}{2}` 

`=  (7×8)^frac{1}{2}` 

`= 56^frac{1}{2}`

`= sqrt56`

Answer :

`= sqrt56`