Step 1 :Given that \(x^{4}=3\)
Step 2 :Square the given equation to find the value of \(x^{8}\), which gives us \((x^{4})^{2}=3^{2}\), simplifying to \(x^{8}=9\)
Step 3 :Subtract 1 from the given equation to find the value of \(x^{4}-1\), which gives us \(x^{4}-1=3-1\), simplifying to \(x^{4}-1=2\)
Step 4 :Final Answer: a) The value of \(x^{8}\) is \(\boxed{9}\). b) The value of \(x^{4}-1\) is \(\boxed{2}\).