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:

The expression is given as,

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

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

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

Thus, we can see that above calculation is correct.

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

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

Hence, option D is correct.