Question

Which of the following is equal to the square root of the cube root of 6 ?

6 to the power of 1 over 3
6 to the power of 2 over 3
6 to the power of 3 over 2
6 to the power of 1 over 6

Answer 1

6 to the power of 1 over 6

Answer 2

The correct option is 4.

Explanation:

The given interpretation is square root of the cube root of 6. The mathematical expression is

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

It can be written as

`((6)^{(1)/(3))^{(1)/(2)}`

Using the property of exponent, we get

`(6)^{(1)/(3)* (1)/(2)}`
`[\because (x^m)^n=(x)^(mn)]`

Now simplify the power.

`(6)^{(1)/(6)}`

The simplified form of given expression is 6 to the power of 1 over 6. Therefore the correct option is 4.