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 by expressing fractional exponents instead of radicals.

Answer 1

`\sqrt[4]{x} * √(y)`

Explanation:

`\sqrt[8]{x^(2) y^(4) }  = x^{2*(1)/(8)} * y^{4*(1)/(8)} = x^{(1)/(4) } * y^{(1)/(2) } = \sqrt[4]{x} * √(y)`

Answer 2

The required expression is
`x^{(1)/(4)}y^{(1)/(2)}`.

Explanation:

Consider the provided information.

`\sqrt[8]{x^2y^4}`

Fraction exponent rule:
`a^{(x)/(y)}=\sqrt[y]{a^x}`

Now by using the above rule we can solve the above expression as shown.

`(x^2y^4)^{(1)/(8)}`

`x^{2* (1)/(8)}\cdot y^{4* (1)/(8)}`

`x^{(1)/(4)}\cdot y^{(1)/(2)}`

`x^{(1)/(4)}y^{(1)/(2)}`

Hence, the required expression is
`x^{(1)/(4)}y^{(1)/(2)}`.