If the question is to find the zeros of the function, then here is the answer.

We have \(x^{4}(x^{2}−3)^{6}\sin^{2}8x=0\) only when

\(x^{4}=0, or, x^{2}-3)^{6}=0, or, sin^{2}8x=0\)

This is equivalent to

\(x=0, or, x^{2}-3 = 0, or, \sin8x=0\)

We know that sine function is zero for angles nπ,nπ, where nn is an integer. Therefore, we get

\(x=0, or, x=\pm\sqrt3, or, x = \frac{8}{n\pi}.\)

If you need more explanation, or wanted something else then feel free to leave a comment. I will update the answer accordingly.

We have \(x^{4}(x^{2}−3)^{6}\sin^{2}8x=0\) only when

\(x^{4}=0, or, x^{2}-3)^{6}=0, or, sin^{2}8x=0\)

This is equivalent to

\(x=0, or, x^{2}-3 = 0, or, \sin8x=0\)

We know that sine function is zero for angles nπ,nπ, where nn is an integer. Therefore, we get

\(x=0, or, x=\pm\sqrt3, or, x = \frac{8}{n\pi}.\)

If you need more explanation, or wanted something else then feel free to leave a comment. I will update the answer accordingly.