Question

`\sqrt[3]{6} /\sqrt[4]{6}`

a) 6¹/²

b) 6¹/⁴

c) 6⁴/³

d) 6⁷/¹²

Answer 1

a)
`\frac{\sqrt[3]{6} }{\sqrt[4]{6} }    = 6 ^{((1)/(12))`

Explanation:

Here, the given expression is:

`\frac{\sqrt[3]{6} }{\sqrt[4]{6} }`

Now, as we know that :
`\sqrt[a]{m}   =  m ^{((1)/(a)) \\`

Applying same in the given expression, we get:

`\sqrt[3]{6}   =  6 ^{((1)/(3))} \\\sqrt[4]{6}   =  6 ^{((1)/(4)) \\\implies \frac{\sqrt[3]{6} }{\sqrt[4]{6} }} \\ = \frac{6 ^{((1)/(3))}}{ 6 ^{(1)/(4) }}`

Also,
`(x ^m)/(x^n)   =  x ^((m-n))`

Now,
`\frac{6 ^{((1)/(3))}}{ 6 ^{(1)/(4) }}  =  6 ^{((1)/(3))  -((1)/(4)) }} = 6 ^{((1)/(12))`

Hence,
`\frac{\sqrt[3]{6} }{\sqrt[4]{6} }    = 6 ^{((1)/(12))`