Question

Which of the following shows why 6 1/3 is equivalent to 6–√3?

Answer 1

Option (4)

Explanation:

We have to prove:
`6^{(1)/(3) }=\sqrt[3]{6}`

To prove this equation we will take
`6^(k)=e^{(1)/(3)}`

`6^(k)=\sqrt[3]{6}`

`(6^(k))^3=(\sqrt[3]{6})^3`

`6^(3k)=6^1`

By comparing powers of 6 on both the sides,

3k = 1

k =
`(1)/(3)`

Therefore,
`6^{(1)/(3)}=\sqrt[3]{6}`

Hence the equation is true.

Option (4) will be the correct opion.