Question

a students work to simplify is shown below select the statemt which best applies to the sample.mathematical work

Answer 1

D. The work shown above is correct and
`x* \sqrt[6]{x^(7)}` may not be simplified further.

Explanation:

We are given the expression,

`\sqrt[6]{x^(13)}=\sqrt[6]{x^(6)* x^(7)}`

i.e.
`\sqrt[6]{x^(13)}=x* \sqrt[6]{x^(7)}`

Thus,
`\sqrt[6]{x^(13)}=x* \sqrt[6]{x^(7)}`

So, we can see that above calculation is correct.

As, in step 2, right side gives
`\sqrt[6]{x^(6)* x^(7)}=(x^(6))^(1)/(6)* (x^(7))^(1)/(6)=x* \sqrt[6]{x^(7)}`

Therefore, the given work is correct and
`x* \sqrt[6]{x^(7)}` may not be further simplified.

Hence, option D is correct.