Question

64 ki power 1/2 ki power 1/6 ki power 2

Answer 1

$\bf{Question}$ :-

$\sf ({64})^{ { (\frac{1}{2}) }^{ { (\frac{1}{6}) }^{(2)} } }$

$\bf{Solution}$ :-

$\sf ({64})^{ { (\frac{1}{2}) }^{ { (\frac{1}{6}) }^{(2)} } } \\ \\ \sf = ({8})^{\cancel2 \times \frac{1}{\cancel2} \times \frac{1}{6} \times 2 } \\ \\ \sf = ( {8})^{ \frac{1}{6} \times 2 } \\ \\ \sf = ( {2})^{3 \times \frac{1}{6} \times 2} \\ \\ (multiply \: 2 \: and \: 3) \\ \\ \sf= ( {2})^{\cancel6 \times \frac{1}{\cancel6} } \\ \\ \sf = {(2)}^{1} \\ \\ \sf = 2 \: (answer)$

Answer 2

Find : 64 ki power 1/2 ki power 1/6 ki power 2

Step by step explanation :

$\tt{ (64){}^{ (\frac{1}{2}) {}^{ (\frac{1}{6}) } {}^{(2)} } }$

Thus, We can write 64 as the square of 2 numbers i.e

$\tt{64 = 8 {}^{2}}$

Thus,

We get :

$\tt{ (8 {}^{2} ){}^{ (\frac{1}{2}) {}^{ (\frac{1}{6}) } {}^{(2)} } }$

Now,

Using the identity,

$\tt{(a {}^{m}) {}^{n} = {a}^{m \times n}}$

$\therefore(8 ){}^{ \cancel2 \times \frac{1}{ \cancel2} \times \frac{1}{6} \times 2 }$

Thus, Now we get :

$\tt{(8) {}^{ \frac{2}{6} }}$

Now, 2/6 = 1/3 , i.e

$\tt{(8) {}^{ \frac{1}{3} }}$

Now,

We know that,

$\tt{ {a}^{ \frac{1}{3} } = \sqrt[3]{a}}$

Therefore, We need to follow final step i.e :

$\tt{8 { }^{ \frac{1}{3} } = \sqrt[3]{8}}$

Now, We know the cube root of 8 i.e 2

Thus,

$\tt{ \tt{ \sqrt[3]{8}} = 2}$

Thus,

Answer to your question is 2.