Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Simplify:

Answer 1

`y^{(1)/(4)}` or
`\sqrt[4]{y}`, where, y≥0.

Explanation:

The given expression is

`\sqrt[8]{y^2}`

We need to find the simplified form of the given expression.

Convert the radical expression in exponent form.

`(y^2)^{(1)/(8)}`
`[\because \sqrt[n]{x}=x^{(1)/(n)}]`

Using the power property of exponent, we get

`y^{2* (1)/(8)}`
`[\because (a^m)^n=a^(mn)]`

`y^{(2)/(8)}`

`y^{(1)/(4)}`

Convert the exponent form in radical expression.

`\sqrt[4]{y}`

Therefore the simplified form of given expression is
`y^{(1)/(4)}` or
`\sqrt[4]{y}`, where, y≥0.

Answer 2

`\sqrt[4]y`

Explanation:

Absolute value is needed, since y can be a negative number, and even roots of real numbers are not real numbers