Answer:
D. The work shown above is correct and [tex]x\times \sqrt[6]{x^{7}}[/tex] may not be simplified further.
Step-by-step explanation:
We are given the expression,
[tex]\sqrt[6]{x^{13}}=\sqrt[6]{x^{6}\times x^{7}}[/tex]
i.e. [tex]\sqrt[6]{x^{13}}=x\times \sqrt[6]{x^{7}}[/tex]
Thus, [tex]\sqrt[6]{x^{13}}=x\times \sqrt[6]{x^{7}}[/tex]
So, we can see that above calculation is correct.
As, in step 2, right side gives [tex]\sqrt[6]{x^{6}\times x^{7}}=(x^{6})^\frac{1}{6}\times (x^{7})^\frac{1}{6}=x\times \sqrt[6]{x^{7}}[/tex]
Therefore, the given work is correct and [tex]x\times \sqrt[6]{x^{7}}[/tex] may not be further simplified.
Hence, option D is correct.
