Question

find the value of (1).49 POWER 1/2 (2). 243 power 2/5 (3). 9 POWER-3/2​

Answer 1

1. $49^{\dfrac{1}{2} }$

We have to find, the value of $49^{\dfrac{1}{2} }$ .

Solution:

∴ $49^{\dfrac{1}{2} }$

= $(7^2)^{\dfrac{1}{2} }$

= $7^{2.\dfrac{1}{2} }$ [ ∵ $(a^{m} )^n=a^{mn}$]

= 7

Thus, the value of "$49^{\dfrac{1}{2} }$ is 7."

2. $243^{\dfrac{2}{5} }$

We have to find, the value of $243^{\dfrac{2}{5} }$.

Solution:

∴ $243^{\dfrac{2}{5} }$

= $(3^5)^{\dfrac{2}{5} }$

= $3^{5.\dfrac{2}{5} }$ [ ∵ $(a^{m} )^n=a^{mn}$]

= $3^{2}$

= 9

Thus, the value of "$243^{\dfrac{2}{5} }$ is 9."

3. $9^{\dfrac{-3}{2} }$

We have to find, the value of $9^{\dfrac{-3}{2} }$.

Solution:

∴ $9^{\dfrac{-3}{2} }$

= $(3^2)^{\dfrac{-3}{2} }$

= $3^{2.\dfrac{-3}{2} }$ [ ∵ $(a^{m} )^n=a^{mn}$]

= $3^{-3}$

= $\dfrac{1}{3^3}$

= $\dfrac{1}{27}$

Thus, the value of "$9^{\dfrac{-3}{2} }$ is $\dfrac{1}{27}$."

Answer 2

1.Given:

49 POWER 1/2

Solution:

$49^{\frac{1}{2} }$= $(7^{2}) ^{\frac{1}{2} }$                [∵$7^{2}$ = 49]

     = 7                     [∵$(a^{m}) ^{n}$ =$a^{mn}$]

∴49 POWER 1/2 = 7

2. Given:

243 POWER 2/5

Solution:

$243^{\frac{2}{5} }$ = $(3^{5}) ^{\frac{2}{5} }$            [∵ $3^{5}$=243]

       = $3^{2}$                 [∵$(a^{m}) ^{n}$ = $a^{mn}$]

       = 9

∴243 POWER 2/5 = 9

3.Given:

9 POWER -3/2

Solution:

$9^{\frac{-3}{2} }$ = $(3^{2}) ^{\frac{-3}{2} }$           [∵$3^{2}$ = 9]

      = $3^{-3}$                 [∵$(a^{m}) ^{n}$ = $a^{mn}$]

      = $\frac{1}{3^{3} }$                   [∵$a^{-m}$ = $\frac{1}{a^{m} }$ ]

      = $\frac{1}{27}$

∴9 POWER -3/2= 1/27