9th Maths 1.6

Exercise 1.6

Q1. Find : i)

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

$64^frac{1}{2}$ ii)

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

$32^frac{1}{5}$ iii)

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

$125^frac{1}{3}$

Sol. :

i) $64^{\frac{1}{2}}$ $64^frac{1}{2}$
$= {(8^{2})}^{\frac{1}{2}}$ $= (8^2)^(frac{1}{2})$
$= 8^{\frac{1}{2} \times 2}$ $= 8^(frac{1}{2}×2)$
$= 8^{1}$ $= 8^1$
$= 8$ $= 8$

Answer

$= 8$ $= 8$
ii) $32^{\frac{1}{5}}$ $32^frac{1}{5}$
$= {(2^{5})}^{\frac{1}{5}}$ $= (2^5)^frac{1}{5}$
$= 2^{5 \times \frac{1}{5}}$ $= 2^(5×frac{1}{5})$
$= 2$ $= 2$ .

Answer

$= 2$ $= 2$
iii) $125^{\frac{1}{3}}$ $125^frac{1}{3}$
$= {(5^{3})}^{\frac{1}{3}}$ $= (5^3)^frac{1}{3}$
$= 5^{3 \times \frac{1}{3}}$ $= 5^(3×frac{1}{3})$
$= 5$ $= 5$

Answer

$= 5$ $= 5$

Q2. Find : i)

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

$9^frac{3}{2}$ ii)

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

$32^frac{2}{5}$ iii)

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

$16^frac{3}{4}$ iv)

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

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

Sol. :

i) $9^{\frac{3}{2}}$ $9^frac{3}{2}$
$= {(3^{2})}^{\frac{3}{2}}$ $= (3^2)^frac{3}{2}$
$= 3^{2 \times \frac{3}{2}}$ $= 3^(2×frac{3}{2})$
$= 3^{3}$ $= 3^3$
$= 27$ $= 27$ .

Answer

$= 27$ $= 27$
ii) $32^{\frac{2}{5}}$ $32^frac{2}{5}$
$= {(2^{5})}^{\frac{2}{5}}$ $= (2^5)^frac{2}{5}$
$= 2^{5 \times \frac{2}{5}}$ $= 2^(5×frac{2}{5})$
$= 2^{2}$ $= 2^2$
$= 4$ $= 4$

Answer

$= 4$ $= 4$
iii) $16^{\frac{3}{4}}$ $16^frac{3}{4}$
$= {(2^{4})}^{\frac{3}{4}}$ $= (2^4)^frac{3}{4}$
$= 2^{4 \times \frac{3}{4}}$ $= 2^(4×frac{3}{4})$
$= 2^{3}$ $= 2^3$

$= 8$ $= 8$

Answer

$= 8$ $= 8$

iv) $125^{\frac{- 1}{3}}$ $125^frac{-1}{ 3}$

$= {(5^{3})}^{\frac{- 1}{3}}$ $= (5^3)^frac{-1}{ 3}$

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

$= 5^{- 1}$ $= 5^(-1)$

$= \frac{1}{5}$ $= frac{1}{5}$

Answer

$= \frac{1}{5}$ $= frac{1}{5}$

Q3. Simplify : i)

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

$2^frac{2}{3}.2^frac{1}{5}$ ii)

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

$(frac{1}{3^3})^7$ iii)

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

$frac{11^frac{1}{2}}{11^frac{1}{4}}$ iv)

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

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

Sol. :

i) $2^{\frac{2}{3}} {.2}^{\frac{1}{5}}$ $2^frac{2}{3}.2^frac{1}{5}$
$= 2^{\frac{2}{3} + \frac{1}{5}}$ $= 2^(frac{2}{3}+frac{1}{5})$
$= 2^{\frac{10 + 3}{15}}$ $= 2^frac{10+3}{ 15}$
$= 2^{\frac{13}{15}}$ $= 2^frac{13}{15}$

Answer :

$= 2^{\frac{13}{15}}$ $= 2^frac{13}{15}$
ii) ${(\frac{1}{3^{3}})}^{7}$ $(frac{1}{3^3})^7$
$= \frac{1}{3^{3} \times 7}$ $= frac{1}{3^3×7}$
$= \frac{1}{3^{21}}$ $= frac{1}{3^21}$
$= 3^{- 21}$ $= 3^{-21}$

Answer :

$= 3^{- 21}$ $= 3^{-21}$
iii) $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$ $frac{11^frac{1}{2}}{11^frac{1}{4}}$
$= 11^{\frac{1}{2} - \frac{1}{4}}$ $= 11^(frac{1}{2}-frac{1}{4})$
$= 11^{\frac{2 - 1}{4}}$ $= 11^frac{2-1}{4}$
$= 11^{\frac{1}{4}}$ $= 11^frac{1}{4}$

Answer :

$= 11^{\frac{1}{4}}$ $= 11^frac{1}{4}$
iv) $7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$ $7^frac{1}{2}.8^frac{1}{2}$
$= 7^{\frac{1}{2}} \times 8^{\frac{1}{2}}$ $= 7^frac{1}{2}×8^frac{1}{2}$
$= {(7 \times 8)}^{\frac{1}{2}}$ $= (7×8)^frac{1}{2}$
$= 56^{\frac{1}{2}}$ $= 56^frac{1}{2}$

$= \sqrt{56}$ $= sqrt56$

Answer :

$= \sqrt{56}$ $= sqrt56$

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9th Maths 1.6

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NCERT Class 9th solution of Exercise 1.2

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NCERT Class 9th solution of Exercise 1.4

NCERT Class 9th solution of Exercise 1.5

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Exercise 1.6

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