Question

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

Answer 1

Answer:

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

Step-by-step explanation:

The expression is given as,

$\sqrt[6]{x^{13}}=\sqrt[6]{x^{6}\times x^{7}}$

i.e. $\sqrt[6]{x^{13}}=x\times \sqrt[6]{x^{7}}$

Then, $\sqrt[6]{x^{13}}=x\times \sqrt[6]{x^{7}}$

Thus, we can see that above calculation is correct.

The right side of step 2 gives, $\sqrt[6]{x^{6}\times x^{7}}=(x^{6})^\frac{1}{6}\times (x^{7})^\frac{1}{6}=x\times \sqrt[6]{x^{7}}$

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

Hence, option D is correct.