Question

Which expression is equivalent to (256x16)1/4

Answer 1

`4x^(4)`

Explanation:

Given in the question an expression,

`(256x^(16))^(1)/(4)`

As we know that,

`x^{(1)/(4) }= \sqrt[4]{x}`

so

`\sqrt[4]{256x^(16) }`

it could also be written as

`\sqrt{\sqrt{256x^(16) } }`

First to solve inner square root

`\sqrt{256x^(16) } = 16x^(16/2)`

`\sqrt{16x^(8) }`

Second outer square root

`\sqrt{16x^(8)}=4x^(8/2)`=
`4x^(4)`